Altimar Acquisition Corp. III 33rd Floor New York, New York 10019

Exhibit 10.4

EXECUTION VERSION

March 3, 2021

Altimar Acquisition Corp. III

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Ladies and Gentlemen:

This letter (this “Letter Agreement”) is being delivered to you in accordance with the underwriting agreement (the “Underwriting Agreement”) entered into by and among Altimar Acquisition Corp. III, a Cayman Islands exempted company (the “Company”), ▇▇▇▇▇▇▇ ▇▇▇▇▇ & Co. LLC and ▇.▇. ▇▇▇▇▇▇ Securities LLC, as representatives (the “Representatives”) of the several underwriters (the “Underwriters”), relating to an underwritten initial public offering (the “Public Offering”) of 15,525,000 of the Company’s units (including 2,025,000 units that may be purchased pursuant to the Underwriters’ option to purchase additional units, the “Units”), each comprised of one of the Company’s Class A ordinary shares, par value $0.0001 per share (the “Ordinary Shares”), and one-fourth of one redeemable warrant (each whole warrant, a “Warrant”). Each Warrant entitles the holder thereof to purchase one Ordinary Share at a price of $11.50 per share, subject to adjustment. The Units will be sold in the Public Offering pursuant to a registration statement on Form S-1 and a prospectus (the “Prospectus”) filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”). Certain capitalized terms used herein are defined in Section 1.

In order to induce the Company and the Underwriters to enter into the Underwriting Agreement and to proceed with the Public Offering and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, Altimar Sponsor III, LLC (the “Sponsor”) and each of the undersigned (each, an “Insider” and, collectively, the “Insiders”) hereby agree with the Company as follows:

1. Definitions. As used herein, (i) “Business Combination” shall mean a merger, share exchange, asset acquisition, share purchase, reorganization or similar business combination with one or more businesses or entities, (ii) “Founder Shares” shall mean the 3,881,250 Class B ordinary shares of the Company, par value $0.0001 per share, outstanding prior to the consummation of the Public Offering, (iii) “Private Placement Warrants” shall mean the warrants to purchase Ordinary Shares of the Company that will be acquired by the Sponsor for an aggregate purchase price of $5,700,000 (or up to $6,105,000 if the Underwriters exercise their option to purchase additional units), or $1.00 per Warrant, in a private placement that shall close simultaneously with the consummation of the Public Offering (including Ordinary Shares issuable upon conversion thereof), (iv) “Public Shareholders” shall mean the holders of Ordinary Shares included in the Units issued in the Public Offering, (v) “Public Shares” shall mean Ordinary Shares included in the Units issued in the Public Offering, (vi) “Trust Account” shall mean the trust account into which a portion of the net proceeds of the Public Offering and the sale of the Private Placement Warrants shall be deposited, (vii) “Transfer” shall mean the (a) sale of, offer to sell, contract or agreement to sell, hypothecate, pledge, grant of any option to purchase or

otherwise dispose of or agreement to dispose of, directly or indirectly, or establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended, and the rules and regulations of the Commission promulgated thereunder with respect to, any security, (b) entry into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any security, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (c) public announcement of any intention to effect any transaction specified in clause (a) or (b), and (viii) “Charter” shall mean the Company’s Amended and Restated Memorandum and Articles of Association, as the same may be further amended, supplemented or otherwise modified from time to time.

2. Representations and Warranties.

(a) The Sponsor and each Insider, with respect to itself, herself or himself, as applicable, represent and warrant to the Company that it, she or he has the full right and power, without violating any agreement to which it, she or he is a party or by which it, she or he is bound (including, without limitation, any non-competition or non-solicitation agreement with any employer or former employer), to enter into this Letter Agreement and, as applicable, to serve as an officer of the Company and/or a director on the Company’s board of directors (the “Board”), and each Insider hereby consents to being named in the Prospectus, road show and any other materials as an officer and/or director of the Company, as applicable.

(b) Each Insider represents and warrants, with respect to itself, herself or himself, as applicable, that (i) such Insider’s biographical information furnished to the Company (including any such information included in the Prospectus) is true and accurate in all material respects and does not omit any material information with respect to such Insider’s background, (ii) such Insider’s questionnaire furnished to the Company is true and accurate in all material respects, (iii) such Insider is not subject to, or a respondent in, any legal action for, any injunction, cease-and-desist order or order or stipulation to desist or refrain from any act or practice relating to the offering of securities in any jurisdiction, (iv) such Insider has never been convicted of, or pleaded guilty to, any crime (x) involving fraud, (y) relating to any financial transaction or handling of funds of another person or (z) pertaining to any dealings in any securities and is not currently a defendant in any such criminal proceeding and (v) such Insider has never been suspended or expelled from membership in any securities or commodities exchange or association or had a securities or commodities license or registration denied, suspended or revoked.

3. Business Combination Vote. It is acknowledged and agreed that the Company shall not enter into a definitive agreement regarding a proposed Business Combination without the prior consent of the Sponsor. The Sponsor and each Insider, with respect to itself, herself or himself, as applicable, agrees that, if the Company seeks shareholder approval of a proposed initial Business Combination, then in connection with such proposed initial Business Combination, it, she or he, as applicable, shall vote all Founder Shares and any Public Shares held by it, her or him, as applicable, in favor of such proposed initial Business Combination (including any proposals recommended by the Board in connection with such Business Combination) and not redeem any Public Shares held by it, her or him, as applicable, in connection with such shareholder approval.

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4. Failure to Consummate a Business Combination; Trust Account Waiver.

(a) The Sponsor and each Insider hereby agree, with respect to itself, herself or himself, as applicable, that, in the event that the Company fails to consummate its initial Business Combination within the time period set forth in the Charter, the Sponsor and each Insider shall take all reasonable steps to cause the Company to (i) cease all operations except for the purpose of winding up, (ii) as promptly as reasonably possible but not more than ten (10) business days thereafter, redeem 100% of the Public Shares, at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay income taxes, if any (less up to $100,000 of interest to pay dissolution expenses) divided by the number of the then-outstanding Public Shares, which redemption shall completely extinguish Public Shareholders’ rights as shareholders (including the right to receive further liquidation distributions, if any), and (iii) as promptly as reasonably possible following such redemption, subject to the approval of the Company’s remaining shareholders and the Board, liquidate and dissolve, subject in each case to the Company’s obligations under Cayman Islands law to provide for claims of creditors and the requirements of other applicable law. The Sponsor and each Insider agree not to propose any amendment to the Charter (i) that would modify the substance or timing of the Company’s obligation to provide holders of the Public Shares the right to have their shares redeemed in connection with an initial Business Combination or to redeem 100% of the Public Shares if the Company does not complete an initial Business Combination within the time period set forth in the Charter or (ii) with respect to any other provision relating to the rights of holders of Public Shares, unless the Company provides its Public Shareholders with the opportunity to redeem their Public Shares upon approval of any such amendment at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay taxes, if any, divided by the number of the then-outstanding Public Shares.

(b) The Sponsor and each Insider, with respect to itself, herself or himself, as applicable, acknowledge that it, she or he, as applicable, has no right, title, interest or claim of any kind in or to any monies held in the Trust Account or any other asset of the Company as a result of any liquidation of the Company with respect to the Founder Shares held by it, her or him, if any. The Sponsor and each Insider, with respect to itself, herself or himself, as applicable, hereby further waive, with respect to any Founder Shares and Public Shares held by it, her or him, as applicable, any redemption rights it, she or he may have in connection with a Business Combination, including, without limitation, any such rights available in the context of a shareholder vote to approve such Business Combination or a shareholder vote to approve an amendment to the Charter (i) that would modify the substance or timing of the Company’s obligation to provide holders of the Public Shares the right to have their shares redeemed in connection with an initial Business Combination or to redeem 100% of the Public Shares if the Company does not complete an initial Business Combination within the time period set forth in the Charter or (ii) with respect to any other provision relating to the rights of holders of Public Shares (although the Sponsor and the Insiders shall be entitled to liquidation rights with respect to any Public Shares they hold if the Company fails to consummate a Business Combination within the time period set forth in the Charter).

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5. Lock-Up; Transfer Restrictions.

(a) The Sponsor and each Insider, with respect to itself, herself or himself, as applicable, agree that it, she or he shall not Transfer any Founder Shares (the “Founder Shares Lock-Up”) until the earlier of (A) one year after the completion of an initial Business Combination and (B) subsequent to an initial Business Combination, (x) if the closing price of the Ordinary Shares equals or exceeds $12.00 per share (as adjusted for share subdivisions, share capitalizations, reorganizations, recapitalizations and the like) for any 20 trading days within any 30-trading day period commencing at least 150 days after such initial Business Combination, or (y) the date on which the Company completes a liquidation, merger, share exchange or other similar transaction that results in all of the Company’s shareholders having the right to exchange their Ordinary Shares for cash, securities or other property (the “Founder Shares Lock-Up Period”).

(b) The Sponsor and each Insider, with respect to itself, herself or himself, as applicable, agree that it, she or he shall not effectuate any Transfer of Private Placement Warrants or Ordinary Shares underlying such Private Placement Warrants until thirty (30) days after the completion of an initial Business Combination.

(c) Notwithstanding the provisions set forth in Sections 5(a) and (b), Transfers of the Founder Shares, Private Placement Warrants and Ordinary Shares underlying the Private Placement Warrants are permitted (a) to the Company’s officers or directors, any affiliates or family members of any of the Company’s officers or directors, any direct or indirect members or partners of the Sponsor or their respective affiliates, any affiliates of the Sponsor, including to funds affiliated with HPS Investment Partners, LLC (“HPS”), and to direct or indirect members or partners of funds affiliated with HPS or any affiliates thereof, any employees of such affiliates or any funds or accounts advised by the Sponsor or its affiliates, (b) in the case of an individual, by gift to a member of one of the individual’s immediate family or to a trust, the beneficiary of which is a member of the individual’s immediate family, an affiliate of such person or to a charitable organization, (c) in the case of an individual, by virtue of laws of descent and distribution upon death of the individual, (d) in the case of an individual, pursuant to a qualified domestic relations order, (e) by private transfers or by other transfers made in connection with the consummation of a Business Combination at prices no greater than the price at which the Founder Shares, Private Placement Warrants or Ordinary Shares, as applicable, were originally purchased, (f) by virtue of the Sponsor’s organizational documents upon liquidation or dissolution of the Sponsor, (g) to the Company for no value for cancellation in connection with the consummation of a Business Combination, (h) in the event of the Company’s liquidation prior to the completion of a Business Combination or (i) in the event of completion of a liquidation, merger, share exchange or other similar transaction which results in all of the Company’s Public Shareholders having the right to exchange their Ordinary Shares for cash, securities or other property subsequent to the completion of a Business Combination; provided, however, that, in the case of clauses (a) through (f), these permitted transferees must enter into a written agreement agreeing to be bound by these transfer restrictions and the other restrictions contained in this Letter Agreement.

(d) During the period commencing on the effective date of the Underwriting Agreement and ending 180 days after such date, the Sponsor and each Insider, with respect to itself, herself or himself, as applicable, agree that it, she or he shall not, without the prior written consent of the Representatives, Transfer any Units, Ordinary Shares, Warrants or any other securities convertible into, or exercisable or exchangeable for, Ordinary Shares held by it, her or him, as applicable, subject to certain exceptions enumerated in Section 5(e) of the Underwriting Agreement.

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6. Remedies. The Sponsor and each Insider, with respect to itself, herself or himself, as applicable, hereby agree and acknowledge that (i) each of the Underwriters and the Company would be irreparably injured in the event of a breach by the Sponsor or such Insider of its, her or his obligations, as applicable under Sections 3, 4, 5, 7, 10 and 11, (ii) monetary damages may not be an adequate remedy for such breach and (iii) the non-breaching party shall be entitled to injunctive relief, in addition to any other remedy that such party may have in law or in equity, in the event of such breach.

7. Payments by the Company. Except as disclosed in the Prospectus, none of the Sponsor, any director or officer of the Company or any of their respective affiliates shall receive from the Company any finder’s fee, reimbursement, consulting fee, monies in respect of any payment of a loan or other compensation prior to, or in connection with, any services rendered in order to effectuate the consummation of the Company’s initial Business Combination (regardless of the type of transaction that it is).

8. Director and Officer Liability Insurance. The Company shall maintain an insurance policy or policies providing directors’ and officers’ liability insurance, and the Insiders shall be covered by such policy or policies, in accordance with its or their terms, to the maximum extent of the coverage available for any of the Company’s directors or officers.

9. Termination. This Letter Agreement shall terminate on the earlier of (i) the expiration of the Founder Shares Lock-Up Period and (ii) the liquidation of the Company.

10. Indemnification. In the event of the liquidation of the Trust Account upon the failure of the Company to consummate its initial Business Combination within the time period set forth in the Charter, the Sponsor (the “Indemnitor”) agrees to indemnify and hold harmless the Company against any and all loss, liability, claim, damage and expense whatsoever (including, but not limited to, any and all legal or other expenses reasonably incurred in investigating, preparing or defending against any litigation, whether pending or threatened) to which the Company may become subject as a result of any claim by (i) any third party for services rendered or products sold to the Company (except for the Company’s independent registered public accounting firm) or (ii) any prospective target business with which the Company has discussed entering into a transaction agreement (a “Target”); provided, however, that such indemnification of the Company by the Indemnitor (x) shall apply only to the extent necessary to ensure that such claims by a third party for services rendered or products sold to the Company or a Target do not reduce the amount of funds in the Trust Account to below the lesser of (i) $10.00 per Public Share and (ii) the actual amount per Public Share held in the Trust Account as of the date of the liquidation of the Trust Account if less than $10.00 per Public Share due to reductions in the value of the trust assets, in each case, net of interest that may be withdrawn to pay the Company’s tax obligations, (y) shall not apply to any claims by a third party or a Target who executed a waiver of any and all rights to the monies held in the Trust Account (whether or not such waiver is enforceable) and (z) shall not apply to any claims under the Company’s indemnity of the Underwriters against certain liabilities, including liabilities under the Securities Act of 1933, as amended. The Indemnitor shall have the right to defend against any such claim with counsel of its choice reasonably satisfactory to the Company if, within 15 days following written receipt of notice of the claim to the Indemnitor, the Indemnitor notifies the Company in writing that it shall undertake such defense.

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11. Forfeiture of Founder Shares. To the extent that the Underwriters do not exercise their option to purchase additional Units within 45 days from the date of the Prospectus in full (as further described in the Prospectus), the Sponsor agrees to automatically surrender to the Company for no consideration, for cancellation at no cost, an aggregate number of Founder Shares so that the number of Founder Shares will equal 20% of the sum of the total number of Ordinary Shares and Founder Shares outstanding at such time. The Sponsor and each Insider, with respect to itself, herself or himself, as applicable, further agree that, to the extent that the size of the Public Offering is increased or decreased, the Company will effect a share capitalization or a share repurchase, as applicable, with respect to the Founder Shares immediately prior to the consummation of the Public Offering in such amount as to maintain the number of Founder Shares at 20% of the sum of the total number of Ordinary Shares and Founder Shares outstanding at such time.

12. Entire Agreement. This Letter Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby. This Letter Agreement may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument executed by all parties hereto.

13. Assignment. No party hereto may assign either this Letter Agreement or any of its rights, interests, or obligations hereunder without the prior written consent of the other parties. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee. This Letter Agreement shall be binding on the Sponsor, each of the Insiders and each of their respective successors, heirs, personal representatives and permitted assigns and transferees.

14. Counterparts. This Letter Agreement may be executed in any number of original or facsimile counterparts, and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

15. Effect of Headings. The paragraph headings herein are for convenience only and are not part of this Letter Agreement and shall not affect the interpretation thereof.

16. Severability. This Letter Agreement shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the validity or enforceability of this Letter Agreement or of any other term or provision hereof. Furthermore, in lieu of any such invalid or unenforceable term or provision, the parties hereto intend that there shall be added as a part of this Letter Agreement a provision as similar in terms to such invalid or unenforceable provision as may be possible and be valid and enforceable.

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17. Governing Law. This Letter Agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York, without giving effect to conflicts of law principles that would result in the application of the substantive laws of another jurisdiction. The parties hereto (i) agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this Letter Agreement shall be brought and enforced in the courts of New York City, in the State of New York, and irrevocably submit to such jurisdiction and venue, which jurisdiction and venue shall be exclusive, and (ii) waive any objection to such exclusive jurisdiction and venue or that such courts represent an inconvenient forum.

18. Notices. Any notice, consent or request to be given in connection with any of the terms or provisions of this Letter Agreement shall be in writing and shall be sent by express mail or similar private courier service, by certified mail (return receipt requested), by hand delivery or facsimile or the electronic transmission.

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[Signature Page to Letter Agreement—Altimar Acquisition Corp. III]

[Signature Page to Letter Agreement—Altimar Acquisition Corp. III]

[Signature Page to Letter Agreement—Altimar Acquisition Corp. III]

[Signature Page to Letter Agreement—Altimar Acquisition Corp. III]

[Signature Page to Letter Agreement—Altimar Acquisition Corp. III]

[Signature Page to Letter Agreement—Altimar Acquisition Corp. III]

[Signature Page to Letter Agreement—Altimar Acquisition Corp. III]

[Signature Page to Letter Agreement—Altimar Acquisition Corp. III]

[Signature Page to Letter Agreement—Altimar Acquisition Corp. III]

[Signature Page to Letter Agreement—Altimar Acquisition Corp. III]