She is best-remembered on television for her co-starring role in the early 1980s ITV children's fantasy series Into the Labyrinth as the evil witch Belor, and her late 1980s guest role in the BBC soap opera EastEnders as shady mafia affiliate Joanne Francis. She has also been seen in two adventures of Doctor Who: as Toos in The Robots of Death (1977) and as Professor Rachel Jensen in Remembrance of the Daleks (1988), a role she reprised for Big Finish Productions' officially licensed audio drama spin-off series Counter Measures. She was also heard as one of the many voices of Xoanon in The Face of Evil (1977). She had auditioned for the role of the Fourth Doctor's companion Leela but the role went to Louise Jameson. Salem also had a recurring role in the British sitcom French Fields from 1989 to 1991.

In film, she played the role of Miss Moneypenny in the 'unofficial' 1983 James Bond film Never Say Never Again, starring Sean Connery. She also appeared in Michael Crichton's The First Great Train Robbery (1979, another film which starred Connery), as well as supporting roles in The Bitch (1979), Night Train to Murder (1983), After Darkness (1985), Thirteen at Dinner (1985), Salome (1986), God's Outlaw (1987), Succubus (1987), Gods and Monsters (1998), Quicksand (2002) and April's Shower (2003). She can also be heard as the Queen in the English dub of "Hellsing Ultimate OVA IV" (2008).