Palmer is the son of former F1 driver and major UK race circuit owner Jonathan Palmer. His younger brother, Will, is a frontrunner in the British BRDC Formula 4 Championship.
Palmer told the Daily Express newspaper in July 2014 that "I am giving everything I can to win the (GP2) series this year and that includes more work, no social life, strict diet – no girlfriend." After ending his driving career, Palmer became an F1 analyst for BBC and the F1 app alongside Jack Nicholls. He is a regular columnist on the BBC Sport website and is also a special contributor to the official F1 website, offering detailed analysis on racing incidents following each Grand Prix.