Azman grew up in Kuala Lumpur but spent much of his racing career based in London. He began karting in 2012, winning the Rotax Max Challenge Malaysia in the MicroMax category that year and finishing third at the Rotax Max Challenge Asia. Moving into European karting in 2013, he achieved a third-place finish at the ROK Cup International Final in Italy, ahead of future Indy Lights driver Antonio Serravalle. He raced in karts until 2015.
Azman made his single-seater debut with two guest rounds of the 2016-17 Formula 4 South East Asia Championship. In 2017 he competed in the F4 Spanish Championship with MP Motorsport from round two onwards, reaching fifth place twice and ending eleventh in the standings. He also took his first single-seater wins during the 2017-18 Formula 4 South East Asia Championship, finishing fourth overall.
For 2018, Jenzer Motorsport signed him for the Italian F4 Championship, where he scored six points finishes with a best of seventh, finishing seventeenth overall. He simultaneously ran a full-time campaign in the F4 Spanish Championship — starting with Drivex School before switching to MP Motorsport — and took four podiums to finish fourth in the standings.
Azman joined Chris Dittmann Racing for the 2019 BRDC British F3 Championship. After a slow opening half, he took his first win at Brands Hatch and added another at the final round, finishing eleventh overall.
He remained in the championship for 2020 with Carlin, alongside Kaylen Frederick and Guilherme Peixoto. Azman began the year with two wins in three races and added another victory during the Brands Hatch round. By season end he had accumulated multiple wins and six additional podiums, finishing fifth in the standings.
In 2021, Azman moved to the Euroformula Open Championship with CryptoTower Racing, alongside Louis Foster and Filip Kaminiarz. He scored his first podium in the second race at the Algarve International Circuit and enjoyed his best weekend of the season at Spa-Francorchamps, finishing on the rostrum in all three races of the event. He added further podiums at the following round and claimed his sole victory of the series at the Hungaroring. He finished fourth in the championship.
After post-season tests in Valencia with Jenzer Motorsport and Charouz Racing System, Azman signed with Hitech Grand Prix for the 2022 FIA Formula 3 Championship — partnering Red Bull Junior Isack Hadjar and 2020 British F3 champion Kaylen Frederick. In doing so, Azman became the first Malaysian driver to take part in the FIA Formula 3 Championship.
The season proved difficult. Azman was outpaced by both teammates, suffered a collision with Rafael Villagomez at Silverstone, and ended the year without a championship point in 32nd, with a best finish of sixteenth achieved three times.
After leaving Formula 3 at the end of 2022, Azman transitioned to endurance racing. He competed in the 2023 Sepang 12 Hours alongside Reid Harker and Adrian D'Silva, finishing third overall. He also ran the 2023 Porsche Carrera Cup Asia with Sime Darby Racing Team, earning one podium in Sepang and finishing sixth in the standings. He continued with Sime Darby in the 2024 Porsche Carrera Cup Asia.
Azman's career reflects the path of many Southeast Asian drivers navigating the European junior ladder with limited budget. His milestone as the first Malaysian in the FIA Formula 3 Championship — stepping up from a program built largely through Formula 4 and national championships — made him a trailblazer in Malaysian motorsport, even as the season itself did not produce the results his earlier BRDC F3 campaigns suggested were possible.