Morse was married from 1967 until 1976 to Australian actor and Director Sandy Harbutt, with whom she starred in Stone.
Morse won the Australian Film Institute Award for Best Actress in a Leading Role for her performance in the 1976 film Caddie. Her notable screen performances also include roles in the film Picnic at Hanging Rock (1975) and the television miniseries A Town Like Alice. Since her early work with Jim Sharman in the 1960s and 70s – A Taste of Honey, Terror Australis, As You Like It – Morse has worked in over ninety theatre productions.
In 2002 and again in 2008, Morse played the role of Theodora Goodman in Adam Cook's adaptation of Patrick White's The Aunt's Story. Her 2004 performance as Nancy in Bryony Lavery's Frozen for the Melbourne Theatre Company earned her a Helpmann Award for Best Female Actor in a Play nomination.
