Claire Martin grew up in a house "full of music", and claims to have learned all of Judy Garland´s songs by the time she was 12. She cites Ella Fitzgerald´s Song Books as being the life changing influence which inspired her to attend Stage School and later to study singing in both New York and London. Her professional career started with her first engagement, aboard the QE2, where she sang in the Theater Bar for two years .
In 1991, at the age of 21, Martin formed her own jazz quartet, and was signed by the Scottish jazz label Linn Records. Her debut album, The Waiting Game, was extremely well reviewed and was selected by The Times as one of their "Albums of the Year". Later that year, she opened for Tony Bennett at the Glasgow International Jazz Festival.
Martin continued performing and recording, garnering numerous awards and rave reviews, throughout the 1990s and early 2000s, including awards from the British Jazz Awards and BBC Jazz Awards for Best Vocalist. She recorded a total of 11 albums (all on the Linn label). Apart from touring both in the UK and on the Continent, she also works as a co-presenter for Jazz Line Up on BBC Radio 3.
She has collaborated with the jazz composer and performer Sir Richard Rodney Bennett.