Having won the 1983 European Formula Two Championship, including winning the last five races of the season, Palmer was given his début drive for Williams in the team's third car at the 1983 European Grand Prix. Following on from this, Palmer joined RAM for 1984, his the first full season, scoring five top ten finishes but no points.
Moving to Zakspeed for 1985, Palmer only drove in half the races, scoring no points; this was followed up with a second unsuccessful season at the German team.
After almost signing for McLaren in 1987, Palmer joined the Tyrrell team. Over the next three seasons, Palmer scored a total of fourteen points; despite this he won the Jim Clark Trophy in 1987, for drivers of naturally-aspirated cars, in the only year it was awarded.
Having failed to qualify for the 1989 Australian Grand Prix, Palmer found himself without a drive, and signed with McLaren, this time as a test driver, while also competing in the World Sportscar Championship. In 1991, he drove in the British Touring Car Championship, before stopping racing. At this point, Palmer decided to stop racing a focus on his business interests, and commentated on F1 races for the BBC following James Hunt's death in mid-1993 until 1996, after which the BBC lost the rights to F1.
Palmer is currently the CEO of MotorSport Vision, which owns several racing circuits in the UK, including Brands Hatch. He is the father of Jolyon Palmer and Will Palmer, both aspiring drivers.