She started her acting career in the TV film The Rainbow, based on the novel by D.H. Lawrence. She played Harper in the Royal National Theatre's production of Tony Kushner's Angels in America in November 1993. Clare was nominated for 1997 Laurence Olivier Theatre Award for Best Actress in a Supporting Role of 1996 for her performance in Who's Afraid of Virginia Woolf?.
She also played Wendy the narrator and mother of Michael in Fallen Angel, a story about Rosie Byfield, a clergyman's daughter who grows up to be a psychopathic killer, starring Emilia Fox. She has the rare achievement of appearing in two episodes of Midsomer Murders as two different characters. The episodes are entitled Country Matters and Ring Out Your Dead.
In 1991, she played Iris Bentley, sister to Derek Bentley, played by Christopher Eccleston, in the film "Let Him Have It".
She teaches Drama at the Guildhall School of Music and Drama.