He appeared in such plays as Brighton Beach Memoirs, As Is, and On Top of the World. He also wrote plays, and these include Thieving Boy, Like Stars in your Hands and The Blitz Kids. He was a member of The Globos, a musical comedy cabaret group, performing at Sydney's Kinselas nightclub in the mid 1980s. Conigrave and his lover, John Caleo, were diagnosed with HIV in 1985. They remained relatively healthy until 1990. In 1991, John was diagnosed with cancer, and Conigrave nursed him until his death on Australia Day (26 January) 1992, despite fighting his own illness.