Clark was a trustee of the Metropolitan Museum of Art from 1932 to 1945, and from 1950 to his death in 1960. He served as the Met's vice president from 1941 to 1945. He was a founding trustee of the Museum of Modern Art in 1929, and served as chairman of its board of trustees from 1939 to 1946. His chairmanship is remembered primarily for his unpopular 1943 firing of MoMA's founding director, Alfred H. Barr Jr. He also served on the board of Roosevelt Hospital, and on numerous corporate boards.