THE ADVISORS’ INNER CIRCLE FUND III

Aegon Emerging Markets Debt Fund

(the “Fund”)

Supplement dated June 26, 2020 to the Fund’s Summary Prospectus, Prospectus and Statement of Additional Information (“SAI”), each dated January 28, 2020

This supplement provides new and additional information beyond that contained in the Summary Prospectus, Prospectus and SAI, and should be read in conjunction with the Summary Prospectus, Prospectus and SAI.

Effective immediately, the Fund is closed to investments by new investors.

PLEASE RETAIN THIS SUPPLEMENT FOR FUTURE REFERENCE

AAM-SK-004-0100