Brennan was born Patricia Wilkinson in Sydney and had a traditional Anglican upbringing. After completing her medical studies at the University of Sydney, she and her husband, Robert Brennan, travelled to Nigeria where they worked as missionaries. Upon their return to Australia, she became concerned with the status of women in the Anglican Church and founded the Movement for the Ordination of Women. The movement had some success, with the first female priests being ordained in Perth in 1992, although Brennan's home diocese of Sydney continues to refuse to ordain women priests. She was made a Member of the Order of Australia (AM) in 1993, in recognition of her services to the community, particularly as founding president of the Movement for the Ordination of Women.
Brennan died in 2011, aged 66, of pancreatic cancer.
- Obituary: "Dr Patricia Anne Brennan AM (1944-2011)", The Courier-Mail, 17 March 2011.
- BRENNAN, Patricia Anne, It's an Honour, 26 January 1993.
- "Vale Patricia Brennan", Compass, 22 May 2011.
- Brennan, Patricia Anne in The Encyclopedia of Women and Leadership in Twentieth-Century Australia