Crennan was a teacher of English literature and was employed by various patent attorneys in New South Wales and Victoria between 1967–1978. She was admitted as a barrister in New South Wales in 1979 and Victoria in 1980. She was made Queen's Counsel in Victoria in 1989 and in New South Wales in 1990. From 1992–1997, Crennan served as a commissioner of the Human Rights and Equal Opportunity Commission (now the Australian Human Rights Commission), the peak human rights body in Australia.