Exhibit 10.7

Spring Valley Acquisition Corp. III

2100 McKinney Avenue, Suite 1675

Dallas, Texas 75201

September 3, 2025

Spring Valley Acquisition III Sponsor, LLC

2100 McKinney Avenue, Suite 1675

Dallas, Texas 75201

Ladies and Gentlemen:

This letter will confirm our agreement that, commencing on the effective date (the “Effective Date”) of the registration statement (the “Registration Statement”) for the initial public offering of the securities (the “IPO”) of Spring Valley Acquisition Corp. III (the “Company”) and continuing until the earlier of (i) the consummation by the Company of an initial business combination or (ii) the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”), Spring Valley Acquisition III Sponsor, LLC (the “Sponsor”) shall make available to the Company certain office space, utilities and secretarial and administrative support as may be required by the Company from time to time, situated at 2100 McKinney Avenue, Suite 1675, Dallas, Texas 75201 (or any successor location). In exchange therefore, the Company shall pay the Sponsor the sum of $30,000 per month on the Effective Date and continuing monthly thereafter until the Termination Date.

The Sponsor hereby agrees that it does not have any right, title, interest or claim of any kind in or to any monies that may be set aside in a trust account (the “Trust Account”) to be established upon the consummation of the IPO (the “Claim”) and hereby waives any Claim it may have in the future as a result of, or arising out of, any negotiations, contracts or agreements with the Company and will not seek recourse against the Trust Account for any reason whatsoever.

[Signature Page Follows]

[Signature Page to Administrative Services Agreement]