Born in Wimbledon, England, Brabham was the second son of Sir Jack Brabham. Despite his mother’s hopes he would avoid motorsport, he began racing in Formula Ford in both Australia and the UK. He made his racing debut in 1982 at Calder Park Raceway, finishing third in a nine-year-old car, and later broke the lap record at Sandown Raceway in the same vehicle.
Brabham moved to Europe in 1983, competing in the British Formula Ford 2000 Championship for Neil Trundle Racing, finishing 11th overall. He also made his sports car debut at Brands Hatch, sharing a March-Ford 83S with Alo Lawler. In 1984, racing for Penistone Racing, Brabham regularly outperformed teammate Julian Bailey, finishing sixth in the British Formula Ford 2000 Championship. He also achieved his first victory in the Thundersports Series at Snetterton, sharing a Tiga-Ford TS84 with Tim Lee-Davey.
With limited single-seater opportunities in 1985, Brabham continued in Thundersports with TechSpeed Racing, recording five second-place finishes in a Shrike-Ford P15 alongside Divina Galica. In 1986, his father established Jack Brabham Racing, and Gary competed in nine rounds of the British Formula 3 Championship, achieving second place at Silverstone) and finishing fifth in the championship. The following year, with Panasonic backing, he won two races at Silverstone) and Donington Park, ultimately finishing sixth in the championship, his progress curtailed by budget constraints.
During 1987, Brabham made guest appearances in the British Touring Car Championship at Oulton Park and won the MG Maestro Challenge at Silverstone), battling Damon Hill. He also competed in a Ford Escort Celebrity race at Brands Hatch, finishing fourth. He also participated in the 1987 James Hardie 1000 at Bathurst, sharing a BMW M3 with Juan Manuel Fangio II), finishing 16th after a late-race incident for Fangio).
In 1988, Brabham returned to England to race for Bowman Racing in British Formula 3. He secured four wins in a Ralt-Volkswagen RT32, finishing second in the championship to JJ Lehto, and also won the Scottish Superprix and Oulton Park Gold Cup. This performance earned him a Formula One test with Benetton at Jerez.
Brabham moved to International Formula 3000 in 1989, initially losing a drive to Andrea Chiesa, but ultimately winning the British Formula 3000 Championship with Bromley Motorsport, taking four victories. He also made appearances in the International series, achieving a fifth-place finish at Brands Hatch. He finished fifth at the 1988 Formula 3 Macau Grand Prix and sixth in 1989.
Brabham’s Formula One opportunity came with the ill-fated Life team in 1990. He failed to prequalify for two Grands Prix, at Phoenix and Brazil, and left the team after those races, frustrated by the lack of progress. A potential drive with the Brabham team fell through due to contractual issues with Life, with the seat ultimately going to his brother, David.
Following his Formula One stint, Brabham raced in F3000 for Middlebridge Racing in 1990, achieving two third-place finishes, but failing to qualify for races at Pau and Birmingham. He also teamed up with his brother David at the Eastern Creek 500, finishing fourth. In 1991, he won the Sebring 12 Hours with Nissan Performance Technology Inc. alongside Geoff Brabham and Derek Daly. He later raced in the IMSA championship, and contested the Bathurst 1000.
In 1992, at Sebring, the winning 1991 crew of Brabham, Daly, and Geoff Brabham were joined by Arie Luyendyk and finished second, narrowly missing a repeat victory. Brabham raced in CART in 1993 and 1994, becoming the first Australian driver to start the Gold Coast Indy Grand Prix, before retiring from racing in 1995 to become an advanced driving instructor, teaching celebrities such as Rowan Atkinson and Captain Mark Phillips.
In 2009, Brabham pleaded guilty to charges of indecent dealing with a child under 12 years, and his name was suppressed while he served his sentence in high security at Wacol jail. In 2016, he was found guilty of rape and indecent treatment of a child, the offences occurring between 2003 and 2007 in Brisbane, and sentenced to 18 months in jail, but was released after six months following an unsuccessful appeal.