She is a member of the Royal Shakespeare Company, and known for various stage, audio and television roles. After appearing in the two series of Alfresco in 1983 and 1984, her first major television success was as George Bulman's assistant Lucy McGinty in Bulman (1985–87). She played, among other roles, Maureen Connell in Between the Lines (1992–1994); Shona Spurtle in The High Life (1994–95); Madame Sin in In The Red BBC TV (1998) adaptation of the novel; Janice Taylor in Holby City (2000–02), Sharon in The Smoking Room (2004–05); Maeve Brown in EastEnders; clinical psychiatrist Pru Plunkett in Midsomer Murders; and Ailsa in Shoebox Zoo. She also appeared on radio including in the 2002 BBC Radio 4 series The Further Adventures of Sherlock Holmes and as Jean Brash in BBC Radio 4's ongoing McLevy series.
Redmond is also a stage actress, having starred in such theatre productions as The Prime of Miss Jean Brodie in 2003, and is a member of the Royal Shakespeare Company, with whom she appeared as Maria in Twelfth Night in 2007. She played Titania/Hippolyta for Shakespeare's Globe in A Midsummer Night's Dream, in its summer 2008 season.
In 2004, Redmond starred in the BBC TV series Sea of Souls as twin sisters Carol and Helen. Redmond appeared in the Gingers for Justice sketch on The Catherine Tate Show in 2005 and then again in 2006. In 2007 she joined The Bill as Crime Scene Examiner Lorna Hart and in 2010 played one of the leads in David Greig's play Dunsinane, reprising her role for the BBC Radio 3 adaptation on 30 January 2011.
On 26 June 2014, it was announced that Redmond would play a new incarnation of the Rani, a villainous character in the long-running series Doctor Who, originally portrayed on television by Kate O'Mara, who had died earlier that year. Redmond's version of the Rani is to be featured in BBC-licensed audio dramas by Big Finish Productions beginning with The Rani Elite, which was released in December 2014.
In November 2014 Redmond joined Alun Armstrong and William Gaunt in a production of Eugène Ionesco's Exit the King at the Ustinov Studio in Bath.
In 2019, Redmond appeared in the Acorn TV series Queens of Mystery as Jane Stone.