Harrow was born in the Auckland suburb of Mount Eden on 25 August 1943, the daughter of Kennedy Mayo Harrow and Eleanor Joan Harrow (née Stacpoole). She studied at the University of Auckland, and later graduated from RADA in 1968, joining BBC Radio's Repertory Company.

Her first film role was in the Italian film The Devil Is a Woman (1974) starring Glenda Jackson. In 1975 Harrow played Helen Alderson in the film adaptation of James Herriot's book All Creatures Great and Small, starring alongside Simon Ward and Anthony Hopkins. She reprised the role the following year in the sequel It Shouldn't Happen to a Vet, this time opposite John Alderton and Colin Blakely.

In 1978 she guest-starred in The Professionals as a formidable counsel arguing at a Court of Inquiry for the disbandment of CI5 in the second season episode 'The Rack', written by Brian Clemens. In that year she also starred in the BBC2 TV series 1990 as Deputy Controller Lynn Blake.

Harrow played Journalist Kate Reynolds in the horror film Omen III: The Final Conflict (1981) starring Sam Neill, and worked with Neill again in Krzysztof Zanussi's film From a Far Country. She starred in the New Zealand film Shaker Run in 1985, and played Lizzie Dickinson in the BBC series Lizzie's Pictures (1987). She won the Australian Film Institute Award for Best Actress in a Leading Role for her performance in The Last Days of Chez Nous (1992). In 1990, Harrow played the tart-tongued, ignored wife in a cunning family of rich brewers in Sins of the Father, Episode 13 of the Inspector Morse series for ITV, starring John Thaw. That year, she also starred in the ABC-TV miniseries Come In Spinner, and played the role of Imogen Donahue in Agatha Christie's Poirot The Kidnapped Prime Minister. Her most recent television performance in Britain was as Kavanagh's wife Lizzie in the series Kavanagh QC, also starring Thaw. She left the programme after the 3rd series (transmitted in 1997) in order to move to America.

Harrow is known for playing Nancy Astor, the first woman to take her seat in the House of Commons, in the BBC drama Nancy Astor of 1982. It aired in the United States in the PBS series Masterpiece Theatre.

For a decade, she was married to actor Sam Neill. Their son Tim was born in 1983.

Harrow has performed on stage all over America. She took over the central role of Vivian Bearing in the Pulitzer Prize winning play Wit in its long-running off-Broadway production in New York City. She was named 2001 Performer of the Year in Pittsburgh for Medea. Other roles include: Raynevskya in The Cherry Orchard at Yale Rep and the Chautauqua Theatre Company, where she also played Kate Keller in All My Sons. She played Creusa in the Washington Shakespeare Theatre Company's 3/10/2009–4/12/2009 production of Euripides's Ion.

In 2014 she played Marion in the New Zealand television series Step Dave.

In the 2015 New Year Honours, Harrow was appointed an Officer of the New Zealand Order of Merit for services to the dramatic arts.