EXHIBIT 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Altimar Acquisition Corp. III (the “Company”) for the quarterly period ended September 30, 2021, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Tom Wasserman, the Chief Executive Officer and chairman of the board of directors of the Company, certify, pursuant to 18 U.S.C. §1350, as added by §906 of the Sarbanes-Oxley Act of 2002, that, to my knowledge:

1.the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2.the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of and for the period covered by the Report.

Date: November 10, 2021
	By:	/s/ Tom Wasserman
		Name:	Tom Wasserman
		Title:	Chief Executive Officer (Principal Executive Officer) and Chairman of the Board of Directors