4.000% Fixed-to-Fixed Rate Subordinated Notes due 2031 TEXAS CAPITAL BANCSHARES, INC., as Issuer, and U.S. BANK NATIONAL ASSOCIATION, as Trustee, FIRST SUPPLEMENTAL INDENTURE Dated as of May 6, 2021

Exhibit 4.1

4.000% Fixed-to-Fixed Rate Subordinated Notes due 2031

TEXAS CAPITAL BANCSHARES, INC.,

as Issuer,

and

U.S. BANK NATIONAL ASSOCIATION,

as Trustee,

FIRST SUPPLEMENTAL INDENTURE

Dated as of May 6, 2021

TABLE OF CONTENTS

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FIRST SUPPLEMENTAL INDENTURE, dated as of May 6, 2021 (this “Supplemental Indenture”), between Texas Capital Bancshares, Inc., a Delaware corporation (the “Company”), and U.S. Bank National Association, as trustee (the “Trustee”), amending and supplementing the Indenture, dated as of September 21, 2012, between the Company and the Trustee, governing the issuance of subordinated debt securities (the “Base Indenture”). The Base Indenture, as amended and supplemented by this Supplemental Indenture, shall be referred to herein as the “Indenture.”

RECITALS

WHEREAS, the Company has executed and delivered the Base Indenture to the Trustee to provide for the issuance of the Company’s debt securities or other evidence of indebtedness, to be issued from time to time in one or more series as determined by the Company under the Base Indenture;

WHEREAS, Section 9.01 of the Base Indenture provides for the Company and the Trustee to enter into an indenture supplemental to the Base Indenture to establish the forms or terms of Debt Securities of any series as permitted by Section 2.01 and Section 2.05 of the Base Indenture;

WHEREAS, pursuant to Section 2.05 of the Base Indenture, the Company wishes to provide for the issuance of a new series of Debt Securities to be known as the Company’s 4.000% Fixed-to-Fixed Rate Subordinated Notes due 2031 (the “Notes”), with the form, terms, provisions and conditions thereof to be set forth as provided in this Supplemental Indenture; and

WHEREAS, pursuant to Section 9.01 of the Base Indenture, the Trustee is authorized to execute and deliver this Supplemental Indenture, and the Company has requested that the Trustee execute and deliver this Supplemental Indenture.

AGREEMENT

NOW, THEREFORE, in consideration of the covenants and agreements set forth herein and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto hereby agree as follows:

ARTICLE 1

DEFINITIONS

Section 1.1    Relation to Base Indenture.

This Supplemental Indenture constitutes an integral part of the Base Indenture, and supplements and amends the Base Indenture solely with respect to the Notes. To the extent there is any inconsistency between the terms of this Supplemental Indenture and the terms of the Base Indenture, the terms of this Supplemental Indenture shall control.

Section 1.2    Definition of Terms.

For all purposes of this Supplemental Indenture:

(a)    a term not defined herein that is defined in the Base Indenture has the same meaning when used in this Supplemental Indenture;

(b)    the definition of any term in this Supplemental Indenture that is also defined in the Base Indenture shall supersede the definition of such term in the Base Indenture;

(c)     a term defined anywhere in this Supplemental Indenture has the same meaning throughout;

(c)    the singular includes the plural and vice versa and use of any gender includes each other gender;

(d)    headings are for convenience of reference only and do not affect interpretation; and

(e)    the following terms have the meanings given to them in this Section 1.2:

“1940 Act Event” means an event requiring the Company to register as an investment company pursuant to the Investment Company Act of 1940.

“Authenticating Agent” means any Person, which may include the Company, authorized by the Trustee pursuant to Section 2.07 of the Base Indenture to act on behalf of the Trustee to authenticate Securities of one or more series.

“Coupon Rate” means, as of any date, the interest rate applicable on such date pursuant to Section 2.5(a) of this Supplemental Indenture.

“Custodian” means, with respect to any Global Note, the Registrar, as custodian for DTC with respect to such Global Note.

“DTC” has the meaning set forth in Section 2.3(d) of this Supplemental Indenture.

“Event of Default” has the meaning set forth in Section 5.1 of this Supplemental Indenture.

“Federal Reserve Board” means the Board of Governors of the Federal Reserve System.

“Five-year U.S. Treasury Rate” means, as of the Reset Determination Date, the average of the yields on actively traded U.S. treasury securities adjusted to constant maturity, for five-year maturities, for the five business days appearing under the caption “Treasury Constant Maturities” in the most recently published statistical release designated H.15 or any successor publication which is published by the Federal Reserve Board as of 5:00 p.m. (Eastern Time) as of any date of determination, as determined by the calculation agent in its sole discretion. If no calculation is provided as described above, then the calculation agent, after consulting such

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sources as it deems comparable to any of the foregoing calculations, or any such source as it deems reasonable from which to estimate the five-year treasury rate, shall determine the Five-Year Treasury Rate in its sole discretion, provided that if the calculation agent determines there is an industry-accepted successor Five-Year Treasury Rate, then the calculation agent shall use such successor rate. If the calculation agent has determined a substitute or successor base rate in accordance with the foregoing, the calculation agent in its sole discretion may determine the business day convention, the definition of business day and the reset dividend determination date to be used and any other relevant methodology for calculating such substitute or successor base rate, including any adjustment factor needed to make such substitute or successor base rate comparable to the Five-Year Treasury Rate, in a manner that is consistent with industry-accepted practices for such substitute or successor base rate.

“Global Notes” has the meaning set forth in Section 2.4 of this Supplemental Indenture.

“H.15” means the daily statistical release designated as such, or any successor publication, published by the Federal Reserve Board.

“Interest Payment Date” has the meaning set forth in Section 2.5(a) of this Supplemental Indenture.

“Interest Rate Agreement” means any interest swap agreement (including any interest rate and foreign exchange rate swap agreement), cap agreement, floor agreement, collar agreement, interest rate agreement, foreign exchange rate agreements, and similar financial instruments.

“Issue Date” means the date of this Supplemental Indenture.

“Maturity Date” means May 6, 2031.

“Notes” has the meaning set forth in the recitals hereto.

“Paying Agent” means any Person, which may include the Company, authorized by the Company to pay the principal of or any premium or interest on any one or more series of Securities on behalf of the Company.

“Principal Subsidiary Bank” means (i) any bank subsidiary the consolidated assets of which constitute 25% or more of the Company’s consolidated assets and (ii) any other bank subsidiary designated as a “Principal Subsidiary Bank” by the Company’s Board of Directors; provided that if the Federal Reserve Board (or other competent regulatory agency or authority) notifies the Company that the Company’s bank subsidiary that is a principal subsidiary bank applying the tests in clause (i) or (ii) above does not qualify as a “major subsidiary depository institution” within the requirements of the Federal Reserve Board’s risk-based capital rules applicable to bank holding companies, such bank subsidiary will not be a “Principal Subsidiary Bank” from and after the time we receive from the Federal Reserve Board such a notice. As of the date hereof, Texas Capital Bank, N.A., is the sole Principal Subsidiary Bank.

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“Regular Record Date” means, with respect to a May 6 Interest Payment Date, the immediately preceding April 22, and with respect to a November 6 Interest Payment Date, the immediately preceding October 22.

“Reset Date” means May 6, 2026.

“Reset Determination Date” means the day falling two Business Days prior to the Reset Date.

“Senior Indebtedness” is defined to include principal of (and premium, if any) and interest, if any, on, and any other payment due pursuant to, any of the following:

unless, in any case, in the instrument creating or evidencing any such indebtedness or obligation, or pursuant to which the same is outstanding, it is expressly provided that such indebtedness or obligation is not superior in right of payment to the Notes or to other debt that is

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pari passu with or subordinate to the Notes; provided, however, that Senior Indebtedness does not include: (i) the Company’s junior subordinated debentures or related guarantees issued to the Company’s statutory trusts, (ii) the Company’s 6.50% subordinated notes due 2042 issued pursuant to the Base Indenture, or (iii) any indebtedness the terms of which expressly provide that such indebtedness ranks equally with, or junior to, the Notes, including guarantees of such indebtedness.

“Tax Event” means the receipt by the Company of an opinion of independent tax counsel to the effect that as a result of:

(a)    an amendment to or change (including any announced prospective amendment or change) in any law or treaty, or any regulation thereunder, of the United States or any of its political subdivisions or taxing authorities;

(b)    a judicial decision, administrative action, official administrative pronouncement, ruling, regulatory procedure, regulation, notice or announcement, including any notice or announcement of intent to adopt or promulgate any ruling, regulatory procedure or regulation (any of the foregoing, an “administrative or judicial action”); or

(c)    an amendment to or change in any official position with respect to, or any interpretation of, an administrative or judicial action or a law or regulation of the United States that differs from the previously generally accepted position or interpretation;

in each case, which change or amendment becomes effective or which administrative or judicial action is announced on or after the Issue Date, with respect to which there is more than an insubstantial risk that interest payable by the Company on the Notes is not, or, within 90 days of the date of such opinion, will not be, deductible by the Company, in whole or in part, for United States federal income tax purposes.

“Tier 2 Capital Event” means the Company’s good faith determination that, as a result of:

(a)    any amendment to, or change in, the laws, rules or regulations of the United States (including, for the avoidance of doubt, any agency or instrumentality of the United States, including the Federal Reserve Board and other federal bank regulatory agencies) or any political subdivision of or in the United States that is enacted or becomes effective after the Issue Date;

(b)    any proposed change in those laws, rules or regulations that is announced or becomes effective after the Issue Date; or

(c)    any official administrative decision or judicial decision or administrative action or other official pronouncement interpreting or applying those laws, rules, regulations, policies or guidelines with respect thereto that is announced after the Issue Date;

in each case, there is more than an insubstantial risk that the Company will not be entitled to treat the Notes then outstanding as “Tier 2 Capital” (or its equivalent) for purposes of the capital adequacy rules or regulations of the Federal Reserve Board (or, as and if applicable, the capital adequacy rules or regulations of any successor appropriate federal banking agency) as then in effect and applicable to the Company, for so long as any Notes are outstanding.

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The terms “Company,” “Trustee,” “Indenture” and “Base Indenture” shall have the respective meanings set forth in the paragraph preceding the recitals to this Supplemental Indenture.

ARTICLE 2

GENERAL TERMS AND CONDITIONS OF THE NOTES

Section 2.1    Designation and Principal Amount.

There is hereby authorized a series of Debt Securities designated the “4.000% Fixed-to-Fixed Rate Subordinated Notes due 2031,” initially offered in the aggregate principal amount of $375,000,000, which amount shall be as set forth in a Company Order for the authentication and delivery of Notes pursuant to Section 2.07 of the Base Indenture.

Section 2.2    Maturity.

Unless earlier redeemed pursuant to Section 3.2 of this Supplemental Indenture, the date upon which the Notes shall become due and payable at final maturity, together with any accrued and unpaid interest, is the Maturity Date.

Section 2.3    Form, Payment and Appointment.

(a)    Principal, premium, if any, and interest shall be considered paid on the date due if the Paying Agent, if other than the Company or one of its Subsidiaries, holds as of 11:00 a.m. New York City time on the due date money deposited by the Company in immediately available funds and designated for and sufficient to pay all principal, premium, if any, and interest then due.

(b)    No service charge shall be made for any registration of transfer or exchange of the Notes, but the Company may require payment from the Holder of a sum sufficient to cover any tax or other governmental charge that may be imposed in connection therewith.

(c)    The Paying Agent, Authenticating Agent and Registrar for the Notes shall initially be the Trustee.

(d)    The Company initially appoints The Depository Trust Company (“DTC”) to act as Depository with respect to the Global Notes. The Trustee shall act as Custodian with respect to the Global Notes.

(e)    The Notes shall be issuable in minimum denominations of $2,000 and integral multiples of $1,000 in excess thereof in book-entry form only.

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Section 2.4    Global Notes.

The Notes shall be represented by a permanent global certificate (collectively, the “Global Notes”) deposited with, or on behalf of, DTC and registered in the name of Cede & Co. Unless and until certificated notes are issued under the limited circumstances described in the Indenture or this Section 2.4, no Holder shall be entitled to receive a definitive certificate representing the Notes. So long as DTC or any successor depositary or its nominee is the registered owner of the Global Note, DTC or any successor depositary, or such nominee, as the case may be, will be considered to be the sole owner or holder of the notes for all purposes of the Indenture. Beneficial interests in the Global Note will be represented through book-entry accounts of financial institutions acting on behalf of beneficial owners as direct and indirect participants in DTC. Investors may elect to hold interests in the Global Note through DTC either directly if they are participants in DTC or indirectly through organizations that are participants in DTC. In connection with any proposed transfer outside the book entry only system, there shall be provided to the Trustee all information necessary to allow the Trustee to comply with any applicable tax reporting obligations, including without limitation any cost basis reporting obligations under Internal Revenue Code Section 6045. The Trustee may rely on the information provided to it and shall have no responsibility to verify or ensure the accuracy of such information.

Section 2.5    Interest.

(a)    Interest on the Notes will accrue (i) during the period from and including the Issue Date, to, but excluding, the Reset Date, or to, but excluding, the date of earlier redemption, at a fixed rate of 4.000% per annum and (ii) during the period from and including the Reset Date, to, but excluding, the Maturity Date, or to, but excluding, the date of earlier redemption, at a rate per annum that will be the Five-year U.S. Treasury Rate as of the Reset Determination Date plus 3.150% per annum. Interest will be payable semiannually in cash in arrears on May 6 and November 6 of each year, commencing on November 6, 2021. Each such date on which interest is payable is an “Interest Payment Date.”

(b)    Interest shall be computed on the basis of a 360-day year consisting of twelve 30-day months. If any scheduled Interest Payment Date falls on a day that is not a Business Day, the Company shall postpone the interest payment to the next succeeding Business Day, but the payment made on such date will be treated as having been made on the date that the payment was first due, and the Holders of the Notes will not be entitled to any further interest or other payments with respect to such postponement.

(c)    The Company shall be responsible for making calculations called for under the Indenture and the Notes, including but not limited to determination of interest, redemption price, premium, if any, and any other amounts payable on the Notes. The Company shall make the calculations in good faith and, absent manifest error, its calculations will be final and binding on the Holders. The Company shall provide a schedule of its calculations to the Trustee when requested by the Trustee, and the Trustee is entitled to rely conclusively on the accuracy of the Company’s calculations without independent verification. The Trustee shall forward the Company’s calculations to any Holder upon the written request of such Holder. The Trustee, acting in any capacity hereunder, shall have no liability or responsibility for making any calculation called for under the Indenture or the Notes, and shall be entitled to rely conclusively upon the accuracy of the Company’s calculations without independent verification thereof.

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(d)    Unless the Company has delivered a notice of redemption for all outstanding Notes, with such redemption to occur on the Reset Date, the Company shall appoint a calculation agent with respect to the Notes prior to the Reset Determination Date, which calculation agent may be the Company or an Affiliate of the Company. The Five-year U.S. Treasury Rate will be determined by the calculation agent on the Reset Determination Date. Promptly upon such determination, the calculation agent will notify the Company of the interest rate from and after the Reset Date. The Company shall then promptly notify the Trustee in writing of such interest rate. Any determination, decision or election that may be made by the calculation agent hereunder, including any determination with respect to a rate, will be conclusive and binding absent manifest error, may be made in the calculation agent’s sole discretion, and, notwithstanding anything to the contrary herein, shall become effective without consent from any other party. The calculation agent’s determination of any interest rate will be on file at the Company’s principal offices, will be made available to any Holder upon request, and will be final and binding in the absence of manifest error. The Trustee or any Paying Agent will have no obligation to be named as calculation agent.

ARTICLE 3

REDEMPTION AND REPURCHASE OF THE NOTES

Section 3.1    No Sinking Fund.

The Notes are not entitled to the benefit of any sinking fund. Sections 3.06 and 3.07 of the Base Indenture shall not apply to the Notes.

Section 3.2    Optional Redemption and Regulatory Event Redemption.

(a)    On at least 30 days but no more than 60 days prior written notice delivered to the Holders, the Company may redeem the Notes in whole or in part, commencing (i) on the Reset Date, but not prior thereto (except upon the occurrence of the events described in Section 3.2 (b)), and on any interest payment date thereafter, or (ii) at any time during the three-month period prior to the Maturity Date, in each case, at a redemption price equal to 100% of the principal amount of the Notes being redeemed, plus accrued and unpaid interest thereon, if any, to, but excluding, the Redemption Date. If fewer than all of the Notes are to be redeemed at any time, the Notes to be redeemed shall be selected in accordance with 3.03 of the Base Indenture.

(b)    The Notes may not otherwise be redeemed prior to the Maturity Date, except that on at least 30 days but no more than 60 days prior written notice delivered to the Holders, the Company may also, at its option and subject to any prior required approval of the Federal Reserve Board, redeem the Notes, in whole, but not in part, at a redemption price equal to 100% of the principal amount of the Notes being redeemed plus accrued and unpaid interest to, but excluding, the Redemption Date, within 90 days of the occurrence of a Tax Event, Tier 2 Capital Event or a 1940 Act Event.

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(c)    Prior to giving any notice to the Holders pursuant to Section 3.2(b), the Company shall deliver to the Trustee an Opinion of Counsel and an Officers’ Certificate certifying that (i) a Tax Event, Tier 2 Capital Event or a 1940 Act Event has occurred and (ii) the Company is entitled to redeem the Notes in accordance with Section 3.2(b), and the Trustee may conclusively rely on such Opinion of Counsel and Officers’ Certificate.

(d)    If the Company elects to have the Trustee deliver the notice of redemption on the Company’s behalf, then the Company shall have delivered to the Trustee no fewer than 15 days prior to the date such redemption notice is to be delivered (unless the Trustee agrees to a shorter period) an Officer’s Certificate providing such direction and setting forth the information to be stated in such notice as provided in Section 3.03 of the Base Indenture. Any partial redemption will be made in accordance with the DTC’s applicable procedures among all of the Holders. If any Note is to be redeemed in part only, the notice of redemption relating to such Note shall state the portion of the principal amount thereof to be redeemed. The Company shall calculate the redemption price as described in the terms of the Notes to be redeemed and will deliver an Officer’s Certificate to the Trustee setting forth the redemption price and showing the calculation of such in reasonable detail no later than two Business Days prior to the Redemption Date, and the Trustee will not be responsible for such calculation nor shall the Trustee have any duty to monitor the accuracy of any calculations made by the Company, which will be conclusive and binding on the Holders, absent manifest error. A replacement Note in principal amount equal to the unredeemed portion thereof will be issued in the name of the Holder thereof upon cancellation of the original Note. The Notes are not subject to redemption or prepayment at the option of the Holders.

(e)    Any redemption of the Notes will be subject to the prior approval of the Federal Reserve Board in accordance with the Federal Reserve Board’s risk-based capital regulations.

(f)    In addition to the Company’s right to redeem the Notes as set forth above in this Section 3.2, the Company may at any time and from time to time purchase Notes in open market transactions, tender offers or otherwise, subject to the prior approval of the Federal Reserve Board, to the extent such approval is then required.

Section 3.3    Effect of Redemption.

Unless the Company defaults in the payment of the redemption price, on and after the Redemption Date, (a) interest shall cease to accrue on the Notes immediately prior to the close of business on the Redemption Date, (b) the Notes shall become due and payable at the redemption price and (c) the Notes shall be void and all rights of the Holders in respect of the Notes shall terminate and lapse (other than the right to receive the redemption price upon surrender of such Notes but without interest on such redemption price). Following the notice of a redemption, neither the Company nor the Registrar shall be required to register the transfer of or exchange the Notes to be redeemed.

Section 3.4    Redemption Procedures.

On or prior to 11:00 a.m. New York City time on any Redemption Date, the Company shall deposit with the Trustee or with a Paying Agent (or, if the Company is acting as its own

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Paying Agent, segregate and hold in trust) an amount of money sufficient to pay the redemption price of, and (except if the Redemption Date shall be an Interest Payment Date) accrued interest on, all the Notes that are to be redeemed on that date. If the Company gives an irrevocable notice of redemption with respect to the Notes pursuant to Section 3.2 of this Supplemental Indenture in connection with an optional redemption, and the Company has deposited with the Trustee or with the Paying Agent the redemption price of the Notes to be redeemed, then, on the Redemption Date, the Paying Agent shall irrevocably deposit such funds with the Depository. The Company shall also give the Trustee irrevocable instructions and authority to instruct the Depository to pay the redemption price in immediately available funds to the Holders of beneficial interests in the Global Notes. If any Redemption Date is not a Business Day, then the redemption price shall be payable on the next Business Day (and without any interest or other payment in respect of any such delay). Interest to be paid on or before the Redemption Date for any Notes called for redemption shall be payable to the Holders on the Regular Record Date for the related Interest Payment Dates. If any Notes called for redemption are not so paid upon surrender thereof for redemption, the redemption price shall, until paid, bear interest from the Redemption Date at the Coupon Rate then in effect.

Section 3.5    No Other Redemption.

Except as set forth in this Article 3, the Notes shall not be redeemable by the Company prior to the Maturity Date.

ARTICLE 4

FORM OF NOTE

Section 4.1    Form of Note.

The Notes and the Authenticating Agent’s Certificate of Authentication to be endorsed thereon are to be substantially in the forms attached as Exhibit A hereto, with such changes therein as the officers of the Company executing the Notes (by manual or facsimile signature) may approve, such approval to be conclusively evidenced by their execution thereof.

ARTICLE 5

DEFAULTS AND REMEDIES

Section 5.1    Events of Default. This Section 5.1, Section 5.2 and Section 5.3 shall replace Section 6.01 of the Base Indenture with respect to the Notes only.

Each of the following is an “Event of Default” with respect to the Notes (whatever the reason for such Event of Default and whether it is voluntary or involuntary or be effected by operation of law or pursuant to any judgment, decree or order of any court or any order, rule or regulation of any administrative or governmental body):

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Section 5.2    Acceleration of Maturity.

If an Event of Default occurs, the principal amount of all the Notes and premium, if any, together with accrued and unpaid interest, if any, thereon, shall automatically, and without any declaration or other action on the part of the Trustee or any Holder, become immediately due and payable.

A default in the payment of principal of or interest on the Notes or in the Company’s non-performance of any other obligation under the Notes of the Indenture will not constitute an Event of Default under the Indenture and will not give rise to any right of acceleration.

At any time after such an acceleration with respect to the Notes has been made and before a judgment or decree for payment of the money due has been obtained by the Trustee as provided in Article VI of the Base Indenture, the Holders of a majority in principal amount of the Notes then Outstanding, by written notice to the Company and the Trustee, may rescind and annul such acceleration and its consequences if (1) the Company has paid or deposited with the Trustee a sum sufficient to pay (A) all overdue interest on all Notes, (B) the principal of or premium (if any) on any Notes which have become due otherwise than by such acceleration and interest thereon, and (C) all sums paid or advanced by the Trustee under the Indenture, together with any compensation, expenses, disbursements and advances due to the Trustee under the Indenture; (2) all Events of Default with respect to the Notes have been cured or waived as provided in Section 6.06 of the Base Indenture; and (3) the rescission would not conflict with any final judgment or decree of a court of competent jurisdiction. No such rescission shall affect any subsequent default or impair any right consequent thereon.

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Section 5.3    Default in Payment.

In the case of a default (not constituting an Event of Default) in the payment of interest or principal, or premium, if any, which failure to pay continues for 30 days, the Company shall, upon the demand of the Trustee, pay to the Trustee, for the benefit of the Holders, the amount then due and payable on such Notes for principal, and premium, if any, and interest and, to the extent that payment of such interest is legally enforceable, interest on any overdue principal, and premium, if any, and on any overdue interest.

If a Default with respect to Notes (other than a Default constituting an Event of Default) occurs and is continuing, the Trustee may in its discretion proceed to protect and enforce its rights and the rights of the Holders by such appropriate judicial proceedings as the Trustee shall deem most effectual to protect and enforce any such rights, whether for the specific enforcement of any covenant or agreement in the Indenture or the Notes or in aid of the exercise of any power granted therein, or to enforce any other proper remedy.

ARTICLE 6

SUBORDINATION

Section 6.1    Debt Securities Subordinate to Senior Indebtedness.

The Notes shall be subject to Article XIII of the Base Indenture.

ARTICLE 7

MISCELLANEOUS

Section 7.1    Ratification of Indenture.

The Base Indenture, as supplemented by this Supplemental Indenture, is in all respects ratified and confirmed, and this Supplemental Indenture shall be deemed part of the Indenture in the manner and to the extent herein and therein provided.

Section 7.2    Trustee and Agent Not Responsible for Recitals.

The recitals herein contained are made by the Company and not by the Trustee or Agent, and the Trustee and Agent assume no responsibility for the correctness thereof. The Trustee and Agent make no representation as to the validity or sufficiency of this Supplemental Indenture.

Section 7.3    New York Law To Govern; Waiver of Jury Trial.

THIS SUPPLEMENTAL INDENTURE AND EACH NOTE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK. EACH PARTY HERETO HEREBY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY RIGHT IT MAY HAVE TO A TRIAL BY JURY IN RESPECT OF ANY LITIGATION DIRECTLY OR INDIRECTLY ARISING OUT OF, UNDER OR IN CONNECTION WITH THIS SUPPLEMENTAL INDENTURE OR THE NOTES.

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Section 7.4    Separability.

In case any one or more of the provisions contained in this Supplemental Indenture or in the Notes shall be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

Section 7.5    Counterparts.

This Supplemental Indenture may be executed in any number of counterparts, each of which shall be an original, but such counterparts shall together constitute but one and the same instrument.

Section 7.6    Facsimile and PDF Delivery of Signature Pages.

This Supplemental Indenture shall be valid, binding, and enforceable against a party when executed and delivered by an authorized individual on behalf of the party by means of (i) an original manual signature; or (ii) a faxed, scanned, photocopied, or portable document format (“PDF”) of a manual signature. Each faxed, scanned, photocopied, or PDF manual signature shall for all purposes have the same validity, legal effect, and admissibility in evidence as an original manual signature. Each party hereto shall be entitled to conclusively rely upon, and shall have no liability with respect to, any faxed, scanned, photocopied, or PDF manual signature of any other party and shall have no duty to investigate, confirm or otherwise verify the validity or authenticity thereof. For the avoidance of doubt, original manual signatures shall be used for execution or indorsement of writings when required under the Uniform Commercial Code or other signature law due to the character or intended character of the writings.

Section 7.7    Required Notices or Demands.

Pursuant to Section 12.03 of the Base Indenture, the following is designated as the address for notices or communications to the Trustee:

U.S. Bank National Association, as Trustee

▇▇▇▇▇ ▇▇▇▇ ▇▇ ▇▇▇▇▇ ▇▇▇

▇▇▇▇▇▇, ▇▇ ▇▇▇▇▇

Attention: Corporate Trust Administration

Facsimile: (▇▇▇) ▇▇▇-▇▇▇▇.

[Signature pages follow]

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The parties hereto have duly executed this Supplemental Indenture as of the day and year first written above.

[Signature Page to First Supplemental Indenture]

[Signature Page to First Supplemental Indenture]

Exhibit A

[FORM OF FACE OF SECURITY]

[Global Securities Legend]

UNLESS THIS CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION (“DTC”), NEW YORK, NEW YORK, TO THE COMPANY OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND ANY CERTIFICATE ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR SUCH OTHER NAME AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC (AND ANY PAYMENT IS MADE TO CEDE & CO., OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC), ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR OTHERWISE BY OR TO ANY PERSON IS WRONGFUL INASMUCH AS THE REGISTERED OWNER HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.

TRANSFERS OF THIS GLOBAL NOTE SHALL BE LIMITED TO TRANSFERS IN WHOLE, BUT NOT IN PART, TO NOMINEES OF DTC OR TO A SUCCESSOR THEREOF OR SUCH SUCCESSOR’S NOMINEE AND TRANSFERS OF PORTIONS OF THIS GLOBAL NOTE SHALL BE LIMITED TO TRANSFERS MADE IN ACCORDANCE WITH THE RESTRICTIONS SET FORTH IN THE INDENTURE REFERRED TO ON THE REVERSE HEREOF.

[Definitive Securities Legend]

IN CONNECTION WITH ANY TRANSFER, THE HOLDER WILL DELIVER TO THE SECURITY REGISTRAR AND TRANSFER AGENT SUCH CERTIFICATES AND OTHER INFORMATION AS SUCH TRANSFER AGENT MAY REASONABLY REQUIRE TO CONFIRM THAT THE TRANSFER COMPLIES WITH THE FOREGOING RESTRICTIONS.

Exhibit A-1

TEXAS CAPITAL BANCSHARES, INC.

4.000% Fixed-to-Fixed Rate Subordinated Notes due 2031 (the “Notes”)

TEXAS CAPITAL BANCSHARES, INC., a Delaware corporation, promises to pay to             , or registered assigns, the principal sum of                          DOLLARS ($                     ) or such greater or lesser amount set forth on the Schedule of Exchange of Interest in the Global Note attached hereto on May 6, 2031.

Interest Payment Dates: November 6 and May 6.

Record Dates: October 22 and April 22.

Exhibit A-2

IN WITNESS THEREOF, the Company has caused this instrument to be duly executed.

Dated:

Exhibit A-3

TRUSTEE’S CERTIFICATE OF AUTHENTICATION

This is one of the 4.000% Fixed-to-Fixed Rate Subordinated Notes due 2031 described in the within-mentioned Supplemental Indenture.

U.S. BANK NATIONAL

ASSOCIATION,

as Trustee

Exhibit A-4

[FORM OF REVERSE SIDE OF SECURITY]

TEXAS CAPITAL BANCSHARES, INC., a Delaware corporation (such corporation, and its successors and assigns under the Indenture hereinafter referred to, being herein called the “Company”), promises to pay interest on the principal amount of this Note at the rate per annum shown above. The Company shall pay interest semiannually in cash in arrears on November 6 and May 6 of each year, commencing on November 6, 2021. Interest on the Notes shall accrue (i) during the period from and including May 6, 2021, to, but excluding, May 6, 2026 (the “Reset Date”), or to, but excluding, the date of earlier redemption, at a rate of 4.000% per annum and (ii) during the period from and including the Reset Date to, but excluding, the Maturity Date, or to, but excluding, the date of earlier redemption, at a rate per annum that will be the Five-year U.S. Treasury Rate as of the Reset Determination Date plus 3.150% per annum. Interest shall be computed on the basis of a 360-day year of twelve 30-day months.

The Company shall pay interest on the Notes (except defaulted interest, if any) to the Persons who are registered holders of Notes at the close of business on the Regular Record Date, whether or not a Business Day, immediately preceding the applicable Interest Payment Date, even if Notes are canceled after the record date and on or before the Interest Payment Date. Holders must surrender Notes to the Paying Agent to collect principal payments. The Company shall pay principal and interest in money of the United States that at the time of payment is legal tender for payment of public and private debts. Payments in respect of the Notes represented by a Global Note (including principal, premium, if any, and interest) shall be made by wire transfer in immediately available funds in U.S. dollars at the office of the Paying Agent or, if the Notes are not represented by a Global Note, at the office or agency of the Company maintained for such purpose in Dallas, Texas.

The Company issued the Notes under an Indenture (the “Base Indenture”) dated as of September 21, 2012, as amended and supplemented by a First Supplemental Indenture (the “Supplemental Indenture” and together with the Base Indenture, the “Indenture”) dated as of May 6, 2021, between the Company and the Trustee. The terms of the Notes include those stated in the Indenture and those made part of the Indenture by reference to the Trust Indenture Act of 1939 (15 U.S.C. §§ 77aaa-77bbbb) as in effect on the date of the Indenture (the “Act”). Terms defined in the Indenture and not defined herein have the meanings ascribed thereto in the Indenture. The Notes are subject to all such terms, and Holders are referred to the Indenture and the Act for a statement of those terms.

The Notes are unsecured obligations of the Company. The Company shall be entitled to issue additional Notes pursuant to Section 2.05 of the Base Indenture with terms and conditions substantially identical to those of the Notes issued on the Issue Date (except

Exhibit A-5

for the issue date, public offering price and amount and date of the first payment of interest thereon) without the consent of the Holders of the Notes. The Notes issued on the Issue Date and any additional Notes shall be treated as a single series for all purposes under the Indenture, provided that if the Notes issued on the Issue Date and the additional Notes are not fungible for U.S. federal income tax purposes, a separate CUSIP number will be issued for the additional Notes.

The Company may, at its option, redeem the Notes in whole or in part, commencing (i) on the Reset Date, but not prior thereto (except upon the occurrence of certain events specified below), and on any interest payment date thereafter, or (ii) at any time during the three month period prior to the Maturity Date, in each case, at a redemption price equal to 100% of the principal amount of the Notes to being redeemed, plus accrued and unpaid interest thereon, if any, to, but excluding, the Redemption Date, in accordance with Section 3.2 of the Supplemental Indenture.

The Notes may not otherwise be redeemed prior to their maturity date, except that the Company may also, at its option and subject to any prior required approval of the Federal Reserve Board, redeem the Notes, in whole, but not in part, at a redemption price equal to 100% of the principal amount of the Notes being redeemed plus accrued and unpaid interest to, but excluding, the Redemption Date, within 90 days of the occurrence of a Tax Event, Tier 2 Capital Event or a 1940 Act Event, in accordance with Section 3.2 of the Supplemental Indenture.

The Company shall not be required to make mandatory redemption or sinking fund payments with respect to the Notes.

The Indenture or the Notes may be amended or supplemented only as provided in the Indenture.

The Notes are in registered form without coupons in minimum denominations of $2,000 principal amount and integral multiples of $1,000 in excess thereof. A Holder may transfer or exchange Notes in accordance with the Indenture. Every Note presented or surrendered for registration of transfer or for exchange shall (if so required by the Company, Security Registrar or the Trustee) be duly endorsed, or be accompanied by a written instrument of transfer in form satisfactory to the Company, the Security Registrar or the Trustee, as the case may be, duly executed, by the Holder thereof or its attorney duly authorized in writing.

Exhibit A-6

The registered Holder of this Note may be treated as the owner of it for all purposes.

The Company may discharge its obligations under the Notes and the Indenture in accordance with Article XI of the Base Indenture.

The Events of Default relating to the Notes are defined in Section 5.1 of the Supplemental Indenture. Upon the occurrence of an Event of Default, the rights and obligations of the Company and the Holders shall be as set forth in the Indenture.

No recourse for the payment of the principal of or premium, if any, or interest on any Note, or for any claim based thereon or otherwise in respect thereof, and no recourse under or upon any obligation, covenant or agreement of the Company in the Indenture or in any Note, or because of the creation of any indebtedness represented thereby, shall be had, directly or indirectly, against any incorporator, subscriber to the shares of beneficial interest (or capital stock or membership interests (as applicable)), shareholder, stockholder, member, employee, agent, manager, officer, trustee or director, as such, past, present or future, of the Company or the Trustee or of any predecessor or successor corporation, either directly or through the Company or the Trustee or any predecessor or successor corporation, whether by virtue of any constitution, statute or rule of law, or by the enforcement of any assessment or penalty or otherwise; it being expressly understood that this Note and the Indenture and the obligations issued hereunder and thereunder are solely corporate obligations and that no such personal liability whatever shall attach to, or is or shall be incurred by, any incorporator, subscriber to the shares of beneficial interest (or capital stock or membership interests (as applicable)), shareholder, stockholder, member, employee, agent, manager, officer, trustee or director, as such, of the Company or the Trustee or of any predecessor or successor corporation, because of the creation of the indebtedness hereby authorized, or under or by reason of the obligations, covenants or agreements contained in this Note or the Indenture or implied herefrom or therefrom; and that any and all such personal liability of every name and nature, either at common law or in equity or by constitution or statute, of, and any and all such rights and claims against, every such incorporator, subscriber to the shares of beneficial interest (or capital stock or membership interests (as applicable)), shareholder, stockholder, member, employee, agent, manager, officer, trustee or director, as such, because of the creation of the indebtedness hereby authorized, or under or by reason of the obligations, covenants or agreements contained in this Note and the Indenture, any certificate or other writing delivered in connection herewith or therewith, or implied herefrom or therefrom, are hereby expressly waived and released as a condition of, and as a consideration for, the execution of the Indenture and the issuance of the Notes. By accepting this Note, each Holder of this Note agrees to the provisions of this Section 11 and waives and releases all such liability. Such waiver and release is part of the consideration for the issuance of the Notes.

Exhibit A-7

12.     Authentication

This Note shall not be valid until an authorized signatory of the Trustee, or any Authenticating Agent appointed by the Trustee, manually signs the certificate of authentication on the other side of this Note.

Customary abbreviations may be used in the name of a Holder or an assignee, such as TEN COM (=tenants in common), TEN ENT (=tenants by the entireties), JT TEN (=joint tenants with rights of survivorship and not as tenants in common), CUST (=custodian), and U/G/M/A (=Uniform Gift to Minors Act).

The Company has caused CUSIP numbers to be printed on the Notes and has directed the Trustee to use CUSIP numbers in notices of redemption as a convenience to Holders. No representation is made as to the accuracy of such numbers either as printed on the Notes or as contained in any notice of redemption and reliance may be placed only on the other identification numbers placed thereon.

THIS NOTE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

Exhibit A-8

ASSIGNMENT FORM

(Insert assignee’s sec. sec. or tax I.D. No.)

and irrevocably appoint agent to transfer this Security on the books of the Company. The agent may substitute another to act for him/her.

Exhibit A-9

[TO BE ATTACHED TO GLOBAL SECURITIES]

SCHEDULE OF INCREASES OR DECREASES IN GLOBAL NOTE

The following increases or decreases in this Global Note have been made:

Exhibit A-10