His first recording, on which he played the saxophone, was with Hull ska band Akrylykz; the second release on York's Red Rhino Records. Although this record was unsuccessful, it did bring him to the attention of Andy Cox and David Steele of the Beat. Akrylykz toured with the Beat, which led to them, in around 1985, asking him to be the lead singer of their new band Fine Young Cannibals after their old band, the Beat, had broken up. He also was a guest Artist on the Ska City Rockers' "Time Is Tight" single.

In 1987, Gift had his first screen role in the film Sammy and Rosie Get Laid, and also appeared in Out of Order the same year. In 1990 he did his first stage work, playing Romeo in the Hull Truck Theatre's production of Shakespeare's Romeo and Juliet, a production which had a brief run in the United States at the Staller Center for the Arts. He also appeared as a lounge singer (singing songs that were included in the Fine Young Cannibals album The Raw and the Cooked) in the 1987 film Tin Men, directed by Barry Levinson.

In 1989, he appeared in Scandal as Johnny Edgecombe, Christine Keeler's boyfriend.

In 1990, he was named by People magazine as one of the "50 Most Beautiful People" in the world.

In December 1992, he began the first of five appearances as the evil Immortal Xavier St. Cloud in the television series Highlander: The Series, and appeared in an episode of the Yorkshire Television series Heartbeat. He also had a small role as the jazz Saxophonist Eddie Mullen in the mini-series Painted Lady (1997), starring Helen Mirren, and appeared in the movie The Island of the Mapmaker's Wife (2001).

He also appeared in Jools Holland's 20th annual 'Hootenanny' show, which aired overnight on BBC2 on 31 December 2012 / 1 January 2013, the last to be recorded at BBC Television Centre. Gift sang the Fine Young Cannibals hits 'Good Thing' and 'Suspicious Minds'.

Gift was a guest vocalist on Jools Holland's 2013 tour.