FORM OF PRIVATE PLACEMENT WARRANT SUBSCRIPTION AGREEMENT BETWEEN SPRING VALLEY ACQUISITION CORP. III AND THE UNDERWRITERS

Exhibit 10.7

FORM OF PRIVATE PLACEMENT WARRANT SUBSCRIPTION AGREEMENT BETWEEN SPRING VALLEY ACQUISITION CORP. III AND THE UNDERWRITERS

THIS PRIVATE PLACEMENT WARRANT SUBSCRIPTION AGREEMENT, dated as of [•], 2025 (as it may from time to time be amended, this “Agreement”), is entered into by and between Spring Valley Acquisition Corp. III, a Cayman Islands exempted company (the “Company”), and [●] (the “Purchaser”).

WHEREAS, the Company intends to consummate an initial public offering of the Company’s units (the “Public Offering”), each unit consisting of one Class A Ordinary Share, par value $0.0001 per share, of the Company (an “Ordinary Share”), and one-third of one redeemable public warrant, as set forth in the Company’s Registration Statement on Form S-1, filed with the U.S. Securities and Exchange Commission (the “SEC”), File No. 333-289294 (the “Registration Statement”), under the Securities Act of 1933, as amended (the “Securities Act”); and

WHEREAS, the Purchaser has agreed to purchase an aggregate of [●] warrants (or [●] warrants if the over-allotment option in connection with the Public Offering is exercised in full) (the “Private Placement Warrants”), each Private Placement Warrant exercisable for one Ordinary Share at an exercise price of $11.50 per Ordinary Share.

NOW THEREFORE, in consideration of the mutual promises contained in this Agreement and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties to this Agreement hereby, intending legally to be bound, agree as follows:

AGREEMENT

Section 1. Authorization, Purchase and Sale; Terms of the Private Placement Warrants.

A. Authorization of the Private Placement Warrants. The Company has duly authorized the issuance and sale of the Private Placement Warrants to the Purchaser.

B. Purchase and Sale of the Private Placement Warrants.

(i) On the date of the consummation of the Public Offering or on such earlier time and date as may be mutually agreed by the Purchaser and the Company (the “IPO Closing Date”), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, an aggregate of [●] Private Placement Warrants at a price of $0.90 per warrant for an aggregate purchase price of $[●] (the “Purchase Price”), which shall be paid by wire transfer of immediately available funds to the Company at least one business day prior to the IPO Closing Date in accordance with the Company’s wiring instructions. On the IPO Closing Date, upon the payment by the Purchaser of the Purchase Price, the Company, at its option, shall deliver a certificate evidencing the Private Placement Warrants purchased by the Purchaser on such date duly registered in the Purchaser’s name to the Purchaser, or effect such delivery in book-entry form.

(ii) On the date of any closing of the over-allotment option, if any, in connection with the Public Offering or on such earlier time and date as may be mutually agreed by the Purchaser and the Company (each such date, an “Over-allotment Closing Date”, and each Over-allotment Closing Date (if any) and the IPO Closing Date, a “Closing Date”), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, up to [●] Private Placement Warrants (or, to the extent the over-allotment option is not exercised in full, a lesser number of Private Placement Warrants in proportion to the portion of the over-allotment option that is exercised) at a price of $0.90 per unit for an aggregate purchase price of up to $[●] (the “Over-allotment Purchase Price”) which shall be paid by wire transfer of immediately available funds to the Company at least one business day prior to the Over-allotment Closing Date in accordance with the Company’s wiring instructions. On the Over-allotment Closing Date, upon the payment by the Purchaser of the Over-allotment Purchase Price, the Company, at its option, shall deliver a certificate evidencing the Private Placement Warrants purchased on such date duly registered in the Purchaser’s name to the Purchaser, or effect such delivery in book-entry form.

C. Terms of the Private Placement Warrants.

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(i) The Private Placement Warrants shall be substantially identical to the warrants offered in the Public Offering as set forth in the Registration Statement, except that the Private Placement Warrants (a) will be subject to the transfer restrictions described herein, (b) are being purchased pursuant to an exemption from the registration requirements of the Securities, and will become freely tradable only after certain conditions are met or the resale of the Private Warrants is registered under the Securities Act, (c) will be entitled to registration rights pursuant to the Registration Rights Agreement (as defined below), (d) may be exercised by the holders on a cashless basis, (e) will not be redeemable by the Company and (f) will not be exercisable more than five years from the commencement of sales in the Public Offering in accordance with FINRA Rule 5110(g)(8).

(ii) At the time of the closing of the Public Offering, the Company and the Purchaser shall enter into a registration rights agreement (the “Registration Rights Agreement”) pursuant to which the Company will grant certain registration rights to the Purchaser relating to the Private Placement Warrants (and the underlying Ordinary Shares).

Section 2. Representations and Warranties of the Company. As a material inducement to the Purchaser to enter into this Agreement and purchase the Private Placement Warrants, the Company hereby represents and warrants to the Purchaser (which representations and warranties shall survive the Closing Date) that:

A. Incorporation and Corporate Power. The Company is an exempted company duly incorporated, validly existing and in good standing under the laws of the Cayman Islands and is qualified to do business in every jurisdiction in which the failure to so qualify would reasonably be expected to have a material adverse effect on the financial condition, operating results or assets of the Company. The Company possesses all requisite corporate power and authority necessary to carry out the transactions contemplated by this Agreement.

B. Authorization; No Breach.

(i) The execution, delivery and performance of this Agreement and the consummation of the transactions contemplated hereby have been duly authorized by the Company as of the Closing Date. This Agreement constitutes the valid and binding obligation of the Company, enforceable in accordance with its terms, subject to bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law). Upon issuance in accordance with, and payment pursuant to, the terms of this Agreement, the Private Placement Warrants will constitute valid and binding obligations of the Company, enforceable in accordance with their respective terms as of the Closing Date.

(ii) The execution and delivery by the Company of this Agreement, the issuance and sale of the Private Placement Warrants and underlying Ordinary Shares, and the fulfillment of, and compliance with, the respective terms hereof and thereof by the Company, do not and will not as of the Closing Date (a) conflict with or result in a breach of the terms, conditions or provisions of, (b) constitute a default under, (c) result in the creation of any lien, security interest, charge or encumbrance upon the Company’s equity or assets under, (d) result in a violation of, or (e) require any authorization, consent, approval, exemption or other action by or notice or declaration to, or filing with, any court or administrative or governmental body or agency pursuant to the Amended and Restated Memorandum and Articles of Association of the Company in effect on the date hereof or as may be amended at or prior to completion of the contemplated Public Offering, or any material law, statute, rule or regulation to which the Company is subject, or any agreement, order, judgment or decree to which the Company is subject, except for any filings required after the date hereof under federal or state securities laws.

C. Title to Securities. Upon issuance in accordance with, and payment pursuant to, the terms hereof and the warrant agreement to be entered into with Continental Stock Transfer & Trust Company (the “Warrant Agreement”) and the amended and restated memorandum and articles of association of the Company, the Private Placement Warrants and underlying Ordinary Shares will be duly and validly issued, fully paid and nonassessable. On the date of issuance of the Private Placement Warrants, the Ordinary Shares underlying the Private Placement Warrants shall have been reserved for issuance. Upon issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement, the Purchaser will have or receive good title to the Ordinary Shares underlying the Private Placement Warrants, free and clear of all liens, claims and encumbrances of any kind, other than (i) transfer restrictions hereunder, under the letter agreement entered into among the Company and its insiders, and under the other agreements

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contemplated hereby, (ii) transfer restrictions under federal and state securities laws, and (iii) liens, claims or encumbrances imposed due to the actions of the Purchaser.

D. Governmental Consents. No permit, consent, approval or authorization of, or declaration to or filing with, any governmental authority is required in connection with the execution, delivery and performance by the Company of this Agreement or the consummation by the Company of any other transactions contemplated hereby.

E. Regulation D Qualification. Neither the Company nor, to its knowledge, any of its affiliates, members, officers, directors or beneficial shareholders of 20% or more of its outstanding securities, has experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act.

Section 3. Representations and Warranties of the Purchaser. As a material inducement to the Company to enter into this Agreement and issue and sell the Private Placement Warrants to the Purchaser, the Purchaser hereby represents and warrants to the Company (which representations and warranties shall survive each Closing Date) that:

A. Organization and Requisite Authority. The Purchaser possesses all requisite power and authority necessary to carry out the transactions contemplated by this Agreement.

B. Authorization; No Breach.

(i) This Agreement constitutes a valid and binding obligation of the Purchaser, enforceable in accordance with its terms, subject to bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law).

(ii) The execution and delivery by the Purchaser of this Agreement and the fulfillment of and compliance with the terms hereof by the Purchaser does not and shall not as of each Closing Date conflict with or result in a breach by the Purchaser of the terms, conditions or provisions of any agreement, instrument, order, judgment or decree to which the Purchaser is subject.

C. Investment Representations.

(i)The Purchaser is acquiring the Private Placement Warrants (and underlying Ordinary Shares) (collectively, the “Securities”), for the Purchaser’s own account, for investment purposes only and not with a view towards, or for resale in connection with, any public sale or distribution thereof.

(ii)The Purchaser is an “accredited investor” as such term is defined in Rule 501(a)(3) of Regulation D, and the Purchaser has not experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act.

(iii)The Purchaser understands that the Securities are being offered and will be sold to it in reliance on specific exemptions from the registration requirements of the United States federal and state securities laws and that the Company is relying upon the truth and accuracy of, and the Purchaser’s compliance with, the representations and warranties of the Purchaser set forth herein in order to determine the availability of such exemptions and the eligibility of the Purchaser to acquire such Securities.

(iv)The Purchaser did not decide to enter into this Agreement as a result of any general solicitation or general advertising within the meaning of Rule 502(c) under the Securities Act.

(v)The Purchaser has been furnished with all materials relating to the business, finances and operations of the Company and materials relating to the offer and sale of the Securities which have been requested by the Purchaser. The Purchaser has been afforded the opportunity to ask questions of the executive officers and directors of the Company. The Purchaser understands that its investment in the Securities involves a high degree of risk and it has sought such accounting, legal and tax advice as it has considered necessary to make an informed investment decision with respect to the acquisition of the Securities.

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(vi)The Purchaser understands that no United States federal or state agency or any other government or governmental agency has passed on or made any recommendation or endorsement of the Securities or the fairness or suitability of the investment in the Securities by the Purchaser nor have such authorities passed upon or endorsed the merits of the offering of the Securities.

(vii)The Purchaser understands that: (a) the Securities have not been and are not being registered under the Securities Act or any state securities laws, and may not be offered for sale, sold, assigned or transferred unless (1) subsequently registered thereunder or (2) sold in reliance on an exemption therefrom; and (b) except as specifically set forth in the Registration Rights Agreement, neither the Company nor any other person is under any obligation to register the Securities under the Securities Act or any state securities laws or to comply with the terms and conditions of any exemption thereunder. While the Purchaser understands that Rule 144 is not available for the resale of securities initially issued by shell companies (other than business combination related shell companies) or issuers that have been at any time previously a shell company, the Purchaser understands that Rule 144 includes an exception to this prohibition if the following conditions are met: (i) the issuer of the securities that was formerly a shell company has ceased to be a shell company; (ii) the issuer of the securities is subject to the reporting requirements of Section 13 or 15(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”); (iii) the issuer of the securities has filed all Exchange Act reports and material required to be filed, as applicable, during the preceding 12 months (or such shorter period that the issuer was required to file such reports and materials), other than Form 8-K reports; and (iv) at least one year has elapsed from the time that the issuer filed current Form 10 type information with the SEC reflecting its status as an entity that is not a shell company.

(viii)The Purchaser has such knowledge and experience in financial and business matters, knows of the high degree of risk associated with investments in the securities of companies in the development stage such as the Company, is capable of evaluating the merits and risks of an investment in the Securities and is able to bear the economic risk of an investment in the Securities in the amount contemplated hereunder for an indefinite period of time. The Purchaser has adequate means of providing for its current financial needs and contingencies and will have no current or anticipated future needs for liquidity which would be jeopardized by the investment in the Securities. The Purchaser can afford a complete loss of its investment in the Securities.

(ix)The Purchaser understands that the Private Placement Warrants shall bear the legend substantially in the form set forth in the Warrant Agreement.

Section 4. Conditions of the Purchaser’s Obligations. The obligation of the Purchaser to purchase and pay for the Private Placement Warrants is subject to the fulfillment, on or before each Closing Date, of each of the following conditions:

A. Representations and Warranties. The representations and warranties of the Company contained in Section 2 shall be true and correct at and as of such Closing Date as though then made.

B. Performance. The Company shall have performed and complied with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by it on or before such Closing Date.

C. No Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement or the Warrant Agreement.

D. Warrant Agreement. The Company shall have entered into the Warrant Agreement and the Registration Rights Agreement.

Section 5. Conditions of the Company’s Obligations. The obligations of the Company to the Purchaser under this Agreement are subject to the fulfillment, on or before each Closing Date, of each of the following conditions:

A. Representations and Warranties. The representations and warranties of the Purchaser contained in Section 3 shall be true and correct at and as of such Closing Date as though then made.

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B. Performance. The Purchaser shall have performed and complied with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by the Purchaser on or before such Closing Date.

C. Corporate Consents. The Company shall have obtained the consent of its Board of Directors authorizing the execution, delivery and performance of this Agreement and the Warrant Agreement and the issuance and sale of the Private Placement Warrants hereunder.

D. No Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement.

E. Warrant Agreement. The Company shall have entered into the Warrant Agreement and the Registration Rights Agreement.

Section 6. Termination. This Agreement may be terminated at any time after December 31, 2025 upon the election by either the Company or the Purchaser upon written notice to the other party if the closing of the Public Offering does not occur prior to such date.

Section 7. Survival of Representations and Warranties. All of the representations and warranties contained herein shall survive each Closing Date.

Section 8. Definitions. Terms used but not otherwise defined in this Agreement shall have the meaning assigned to such terms in the Registration Statement.

Section 9. Miscellaneous.

A. Successors and Assigns. Except as otherwise expressly provided herein, all covenants and agreements contained in this Agreement by or on behalf of any of the parties hereto shall bind and inure to the benefit of the respective successors of the parties hereto whether so expressed or not. Notwithstanding the foregoing or anything to the contrary herein, the parties may not assign this Agreement, other than assignments by the Purchaser to affiliates thereof (including, without limitation one or more of its members).

B. Severability. Whenever possible, each provision of this Agreement shall be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Agreement is held to be prohibited by or invalid under applicable law, such provision shall be ineffective only to the extent of such prohibition or invalidity, without invalidating the remainder of this Agreement.

C. Counterparts. This Agreement may be executed simultaneously in two or more counterparts, none of which need contain the signatures of more than one party, but all such counterparts taken together shall constitute one and the same agreement.

D. Descriptive Headings; Interpretation. The descriptive headings of this Agreement are inserted for convenience only and do not constitute a substantive part of this Agreement. The use of the word “including” in this Agreement shall be by way of example rather than by limitation.

E. Governing Law. This Agreement shall be deemed to be a contract made under the laws of the State of New York and for all purposes shall be construed in accordance with the internal laws of the State of New York.

F. Amendments. This Agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by all parties hereto.

[Signature Page Follows]

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IN WITNESS WHEREOF, the parties hereto have executed this Agreement to be effective as of the date first set forth above.

COMPANY:

SPRING VALLEY ACQUISITION CORP. III

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PURCHASER:

[●]

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[Signature Page to Private Placement Warrant Subscription Agreement]