Tappy began his racing career in karting, finishing runner-up in the 2004 UK Formula Ford championship winter series.

During this year he also won the end-of-season Formula Ford Festival and was selected as a finalist for the prestigious McLaren Autosport BRDC award.

In 2006 Tappy stepped up to the British Formula Renault 2.0 Championship with Jamun Racing, finishing his debut year eighteenth in the standings.

He transferred to Fortec Motorsport for the 2007 season, taking sixteen podium finishes, including nine race wins, to end the year as series champion.

He returned to sports car racing in 2012, competing in the Blancpain Endurance Series for ART Grand Prix alongside Grégoire Demoustier.