Sims began kart racing in 1998, winning the Super 1 MSA Cadet Championship and the Kartmasters Grand Prix in 2000 before accumulating further titles including the JICA British Championship and the Formula A World Championship. He made the step to single-seaters in late 2006 via the Formula Renault UK Winter Series, where he scored a second place on debut.
In the main Formula Renault 2.0 UK series he raced with Manor Competition in 2007 and 2008. His 2008 campaign was particularly unlucky: he accumulated the most raw points across the season but the championship's drop-score rules — dropping the two worst results — swung a one-point deficit into a 23-point loss to Adam Christodoulou. In December 2008 Sims won the McLaren Autosport BRDC Award for promising young British drivers.
Moving to the Formula 3 Euro Series for 2009 with Mücke Motorsport, Sims finished fourth in the championship — a season dominated by Jules Bianchi — taking one win at the Nürburgring and four second places. He joined ART Grand Prix for 2010.
Sims returned to single-seater racing with a partial 2013 GP3 Series campaign. He first deputised at the Nürburgring round for Status Grand Prix, replacing Adderly Fong. He then contested the final three rounds with Carlin, stepping in for Eric Lichtenstein. Despite participating in only half the season's race weekends, he secured one victory and two further podiums, finishing eighth in the final standings — a strong return on limited mileage in the series.
Sims' career diversified substantially after his single-seater years. He drove a Lola-Judd LMP2 at the 2012 24 Hours of Le Mans for Status Grand Prix and raced in the Blancpain Endurance Series. In 2016 he took outright victory at the 24 Hours of Spa with Rowe Racing in a BMW M6.
He entered Formula E with BMW i Andretti Motorsport from Season 5, partnering Antonio Felix da Costa. At the 2019 New York City ePrix season finale, Sims claimed pole position and a podium finish. He then won his first Formula E race at the second Diriyah ePrix in the 2019–20 season. After a move to Mahindra Racing for 2020–21, where he added a podium at the Rome ePrix, Sims departed Formula E after the 2021–22 season.
Sims joined Whelen Engineering Racing in the IMSA SportsCar Championship and won the 2023 IMSA SportsCar Championship title, the pinnacle of his career to date. He subsequently moved to Corvette Racing by Pratt Miller Motorsports. His trajectory — from an unlucky Formula Renault championship runner-up to a transatlantic sportscar champion — illustrates how talent overlooked by narrow single-seater pathways can flourish in endurance and electric racing.
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