Hammond began her career on stage and made early appearances on television shows such as Softly, Softly (1968) and The Trouble Shooters (1969). Her first leading role was as Lady Macbeth at the Roundhouse in 1970 in Peter Coe's African version of the play. She went on to star in many plays by an array of up-and-coming black writers: Sweet Talk by Michael Abbensetts, 11 Josephine House by Alfred Fagon and several plays written by Mustapha Matura including As Time Goes By, Play Mas and Playboy of the West Indies. She also spent two years at the Royal National Theatre in productions including Fuente Ovejuna and Peer Gynt directed by Declan Donnellan, and The Crucible.