Grant made her debut on the Great White Way in a 1963 production of Tambourines to Glory by Langston Hughes. In the 1970s, Grant wrote and starred in Don’t Bother Me, I Can’t Cope, a musical revue that received four Tony nominations. She also became the first woman to write the music and lyrics to a Broadway musical.
By that time, she'd already made history on Another World, playing attorney Peggy. Deadline cited a book by Ellen Holly (ex-Carla, One Life to Live), who said that Peggy was originally written as a white character. Once Grant was cast, she became the first Black contract player in daytime television history.
Grant starred on AW from 1965 to 1972, during which time Peggy was involved in what is credited as the first regular daytime storyline specifically penned for a Black actress. Grant also appeared on The Edge of Night, All My Children, and Guiding Light. Her work garnered her Obie, NAACP Image, and Grammy Awards.