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

I, Michael Occi, the Chief Executive Officer (Principal Executive Officer) of North Haven Private Income Fund A LLC (the “Company”), hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

•the Form 10-K of the Company for the year ended December 31, 2025 as filed with the Securities and Exchange Commission on the date hereof (the “Form 10-K”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

•the information contained in the Form 10-K for the year ended December 31, 2025 fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: March 3, 2026
/s/ Michael Occi
Michael Occi Chief Executive Officer (Principal Executive Officer)