Clarke made his circuit racing debut in 2006 in the Formula BMW UK one-make series, driving for Nexa Racing. The season was difficult by his own account; he scored only two points, finishing 22nd in the championship and sixth in the Rookie Cup, and also competed in the end-of-season World Final in Valencia where he placed 25th. During the same year he sat his A levels at the City of London Freemen's School in Ashtead, Surrey.
For 2007, Clarke moved up to the Formula Palmer Audi series. After a subdued start to the season, he accumulated seven podium finishes across the final thirteen rounds, including victories at Brands Hatch and Croft, to climb to fourth in the championship, holding off Jason Moore by two points. He also contested that year's Autumn Trophy, finishing third behind champion Richard Keen. Clarke remained in Formula Palmer Audi in 2008, finishing fifth in the championship with wins at Oulton Park and Brands Hatch and a fourth-place Autumn Trophy campaign featuring a win and two poles.
Clarke stepped up to the FIA Formula Two Championship in 2009, racing car number eleven. He was involved in the accident at the Brands Hatch round that July in which fellow competitor Henry Surtees lost his life: Clarke lost control exiting Westfield bend, spinning into the tyre wall; one of the wheels detached and bounced back onto the circuit, striking Surtees's head. Clarke paid public tribute to Surtees, describing him as a "quality driver" and a "hard racer." Clarke scored six points over the course of the season and finished eighteenth overall.
He remained in Formula Two in 2010, improving significantly with two podiums and 81 championship points to finish ninth. He continued in the championship in 2011 as well.
In 2012, Clarke made three appearances in North American stock car racing. He started the No. 14 Toyota for X Team Racing in a NASCAR K&N Pro Series East event at Rockingham Speedway, starting 14th and finishing 19th. He also entered one K&N Pro Series West race for Andy Woolgar at NAPA Speedway in No. 74 Dodge, starting 17th and finishing 20th, and attempted a further West Series race at All American Speedway without qualifying. In the ARCA Racing Series that year, he started 22nd and finished 30th at Salem Speedway driving a No. 97 Dodge for Creation-Cope Racing, his race ending in a crash.
In 2014, Clarke entered the British Touring Car Championship with Crabbie's Racing in a Ford Focus. His best result during that single campaign was a second-place finish at the Brands Hatch final round.
Clarke retired from racing at the end of the 2014 season. He subsequently co-founded driver management company Veloce Sport alongside former racing driver Rupert Svendsen-Cook and his step-sister Mariella Bailey.