Tappy began his career like most racers in karting and was active until 2003 in this sport. In 2003, he also gave his debut in Formula racing in the British Formula Zip, which he finished in eleventh place. In 2004 he came only towards the end of the year in the British Formula Ford Winter Series and won the runner-up title. In 2005 he started for Jamun Racing in the regular championship of the British Formula Ford and won half of the race. Despite the many victories, it was enough for the British not to the championship title and he was behind his teammate Charlie Donnelly runner-up.
2006 remained Tappy at Jamun Racing and participated in the British Formula Renault. In his first season he finished in 18th place overall. In 2007 he sang his second season for Fortec Motorsport. The Briton won 9 of 20 races and won ahead of his teammate Dean Smith the title. He also took part in races of northern European and French Formula Renault.
After the Briton had participated for the British team in A1 Grand Prix test drives in early 2008, he competed in sports car racing. He went to a race in the Le Mans Series and two races of the British Porsche Carrera Cup. Then he returned to Formula racing and replaced Borja García at RC Motorsport in the World Series by Renault. Overall, he completed eight races and finished the season at the 23rd place overall. In addition, he competed in ten out of twelve races in the first season of Superleague Formula, a racing series, competing in the football clubs with racing car, for assisted GTA Motor Competición team of Tottenham Hotspur. A second place was his best result.
In 2009, Tappy participate only in individual races of different racing series. He first started in the first two races of the North American Indy Lights and came not with two races to the finish. He then participated in the first two races of the International Formula Master in part. After being used in this series in any other race, he went to for assisted by Ultimate Motorsport team of Galatasaray Istanbul at the first four races of the Superleague Formula. 2010 Tappy received a cockpit for one season in the Auto GP at DAMS. With a second place as best result he finished at the end of the season behind his team-mate Romain Grosjean and Edoardo Piscopo third overall. He also starts at some races in the Super League Formula 2010 season for assisted Alpha Motorsport team Flamengo Rio de Janeiro. After the tenth race weekend Tappy was a total of five times on the podium. A victory he did not succeed.
In the years 2005 and 2007 Tappy was nominated for the McLaren Autosport BRDC Award, but was never awarded the prize.
- 2003: British Formula Zip ( place 11 )
- 2004: British Formula Ford Winter Series (2nd place)
- 2005: British Formula Ford (No. 2 )
- 2006: British Formula Renault ( 18th place)
- 2007: British Formula Renault (Master)
- 2008: World Series by Renault ( No. 23 ); Superleague Formula; Le Mans Series ( No. 19 )
- 2009: Superleague Formula; International Formula Master ( No. 22 ); Indy Lights ( # 32 )
- 2010: Auto GP ( 3rd place); Superleague Formula