Callum was born in Cambridge, UK, on 11 November 1998.
Callum had his first drive in a kart just before his seventh birthday. At 12 years old he became the under 16s Formula Kart Stars British Champion and finished 3rd in the German KFJ National Championship. At 13, Callum dominated the international under 15s KFJ category, winning the WSK Masters Series, the WSK Final Cup, and was runner-up in both the WSK Euro Series and the CIK-FIA World Cup. As a 15 year old, in 2014 Callum become the senior CIK-FIA European Karting Champion, he won the seniors WSK Super Master Series, and finished 4th out of 32 competitors in the CIK-FIA World Championship.
Callum made an unusual debut in single-seater racing at 16, jumping straight from karting up to F3, competing in the FIA F3 European Championship for three years. In his first season he finished 12th overall, out of a grid of 35 seasoned drivers, and then finished 6th overall in 2016 with two wins for Van Amersfoort Racing (Paul Ricard and Spielberg).
In 2017, Callum joined the FDA and took 6 wins (Silverstone, Monza, Hungaroring, Zandvoort, Spielberg and Hockenheim), 11 podiums and 10 pole positions in the FIA F3 European Championship, finishing 4th overall. He rounded off his 2017 F3 campaign with a win in the FIA F3 World Cup Qualification Race at the Macau GP street circuit. In 2018 he competed for ART Grand Prix in GP3 ending the season in third with two wins (Paul Ricard and Spielberg) and 167 points. In 2019, he took part in the FIA Formula 2 series with the Sauber Junior Team by Charouz Racing, taking pole at Monza and two third places in Barcelona and Sochi. He also finished a further eight times in the points on his way to eleventh in the championship.
In 2020, he was the Formula 2 runner-up, driving for UNI-Virtuosi Racing, taking three wins and five pole positions (the most of any driver). At the end of the year it was announced he would take on the role of Scuderia Ferrari test driver for 2021.