Fewtrell started his karting career in 2009 at the age of ten where he managed to rack up a few points before claiming third in the 2014 Deutsche Junior Kart Meisterschaft and second in 2014 South Garda Winter Cup KF3. Max claimed his first title win in 2014 at the 25 degree Trofeo Andrea Margutti KFJ. He took home a further two titles when he claimed second in the WSK Champions Cup KFJ and third in the 2015 Andrea Margutti Trophy KF. Following from his success in karting, Fewtrell moved to single-seaters in 2015 where he raced in the MRF Challenge, finishing eleventh. Heading into 2016, Max joined Carlin for a campaign in British F4 where he took three victories, claiming the championship in the final race at Brands Hatch. Alongside his three wins, he claimed 16 podiums, 3 pole positions and 4 fastest laps, racking up a totle of 358 points.
In the December of 2016, he joined Tech 1 Racing for the 2017 season of Formula Renault 2.0, winning a race at the Red Bull Ring and taking sixth in the drivers championship. He made the move to the reigning team champions, R-ace GP, the following year where he achieved six wins where he became the first driver since Formula E driver Nyck de Vries to claim a double victory across a two race weekend while also claiming six pole positions. Fewtrell was awarded the title in the season finale, just 17 and a half points clear of Christian Lungaard.
In 2017, Max signed as a part of the Renault Sports Academy Line Up.
FIA Formula 3
During 2019, Max raced with ART Grand Prix in his debut year of the FIA Formula 3, alongside teammate Lundgaard. He managed to pull out two podiums and 57 points, leaving him 10th in the drivers standings. Alongside FIA F3, Fewtrell raced in the F3 Asian Winter Series with Dragon Hitech GP where he finished 11th and the Macau Grand Prix with Hitech GP where he finished 18th
Heading into the 2020 season, Max is making his return to FIA Formula 3 for his second year with Hitech Grand Prix alongside teammates Liam Lawson and rookie, Dennis Hauger.