Simpson made his car racing debut in 2020 for Velocity Racing Development in the Formula 4 United States Championship, after nine years of karting across the Caribbean and United States. He simultaneously entered the Formula Regional Americas Championship that year, and dominated the championship in his second season in the series, taking podiums in all but five races. Winning the FR Americas title earned Simpson a Honda Performance Development scholarship worth $600,000 towards a Super Formula campaign in 2022; Japan's travel restrictions due to COVID-19 prevented those plans.
Alongside his Regional F3 campaign, Simpson entered the Road to Indy ladder with Juncos Racing in the Indy Pro 2000 Championship, contesting sixteen of the eighteen races and scoring three podiums.
In 2022, Simpson signed a multi-year development driver deal with Chip Ganassi Racing and progressed to Indy Lights with TJ Speed Motorsports alongside James Roe Jr. After eight races he moved to HMD Motorsports, finishing ninth in the standings with a best result of fifth at Barber and Detroit. Simpson returned to the rebranded Indy NXT series in 2023 with HMD Motorsports, scoring two podiums and ending up tenth overall.
Simpson made his IMSA debut at the 2022 24 Hours of Daytona with Gradient Racing in an Acura NSX GT3 EVO II. Later that year, he and teammates Mario Farnbacher and Till Bechtolsheimer won the 2022 Petit Le Mans in the GTD class.
In 2023, Simpson joined Tower Motorsports for a part-time LMP2 campaign. After finishing fifth at the 24 Hours of Daytona, he and teammates Scott McLaughlin and John Farano won the LMP2 class of the 12 Hours of Sebring — his second triumph in IMSA.
Simpson competed full-time in the 2023 Asian Le Mans Series with Algarve Pro Racing alongside James Allen and John Falb, in preparation for the European Le Mans Series campaign. The season opener in Dubai yielded victory despite a spin from Falb; Simpson played a major role, taking second place from Indy NXT rival Christian Bogle near half-distance and reducing a gap of 25 seconds to Ayhancan Güven to seven seconds by the end of his stints. A puncture at the following race prevented a win; they finished fourth. At the Yas Marina Circuit, race one saw Simpson battle Oliver Jarvis for a podium before spinning into the turn-sixteen wall shortly before the end. Fourth on Sunday left the trio third in the LMP2 classification.
Simpson remained with Algarve Pro Racing for the 2023 European Le Mans Series, again partnering James Allen; Cadillac Hypercar driver Alex Lynn joined as the third driver. An unspectacular maiden race at Barcelona was followed by a marked improvement at Circuit Paul Ricard: Simpson stayed close to leader Vladislav Lomko throughout the opening stints — setting the race's fastest lap — enabling Lynn and Allen to battle for victory, with Allen executing a late-race pass on Louis Delétraz. Prior to the third race at Aragón, Alex Lynn praised Simpson, calling him "a fast learner" and commending his pace while noting he needed more experience; the team finished third. In a chaotic Spa event the trio drove an error-free race to take victory and move into the championship lead. A pair of second places at the 4 Hours of Algarve and Portimão secured the ELMS title. At Portimão, Simpson struggled in wet conditions but kept the car on track while others did not.
In January 2023, Simpson completed his first NTT IndyCar Series test with Chip Ganassi Racing at Sebring International Raceway. After the 2023 IndyCar season, Chip Ganassi announced Simpson would step up to IndyCar in 2024. He began his debut season at St. Petersburg with a twelfth-place finish, ending ahead of all other rookies and setting the fastest lap of the race. He recorded three further top-twenty finishes before finishing 21st at the Indy 500, having qualified a then-record eighteenth. Two retirements followed: a spin into the barriers caused by Christian Rasmussen at Road America, and a spin from Agustín Canapino in Monterey. Two top-twenty results at Iowa were followed by a retirement in Toronto after crashing at turn eight with seventeen laps remaining. At Gateway he spun into the wall on lap 86 after struggling for pace. After sixteenth at Portland, he took thirteenth in the second Milwaukee race and finished 22nd at Nashville. Simpson ended 21st in the drivers' standings, behind all four teammates; he was retained for 2025 and moved to the No. 8.
Simpson started eighteenth at St. Petersburg and fifteenth at Thermal Club. He claimed his maiden IndyCar top-ten at Long Beach, finishing tenth on the alternate strategy. Having qualified tenth at Barber, he finished one lap down in 21st; he qualified tenth again for the Indy Road Course race but could not start due to mechanical trouble on his way to the grid. He qualified thirteenth for the Indy 500 but was taken out mid-race after being clipped by a spinning Kyle Larson. The following weekend at Detroit, Simpson posted the fastest lap and finished fifth on the alternate strategy. A fifteenth at Gateway preceded sixth at Road America. After qualifying third at Mid-Ohio, a pit-lane stall and a penalty for running over a crew member from Rinus Veekay's crew left him tenth. The Iowa double-header brought eighteenth and thirteenth finishes. At Toronto, having qualified fourteenth and started thirteenth, Simpson ran a two-stop strategy to charge through the field and finish third — his first IndyCar podium. He retired from the Monterey round on the opening lap after causing a collision with Felix Rosenqvist at turn 6 and received a six-place grid penalty for the following event at Portland, where he dropped from qualifying to 21st in the race. An unremarkable Milwaukee race ended twentieth. At the Nashville finale, having qualified tenth, Simpson battled Scott McLaughlin for a podium in the final laps before being re-overtaken on the last lap and finishing fourth — his best oval result to date. McLaughlin later praised Simpson's racecraft, calling him someone who "respected the outside lane". Simpson improved to 17th in the standings with six top-ten finishes.
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