Moore began his motorsport career in karting, where he was active until 2007. In 2007, he also gave his debut in GT racing. He immediately became masters of British Ginetta Junior Championship. 2008 Moore joined the British Ginetta G50 Cup and won with 14 wins from 19 races the championship. He also participated in several races of the British GT Championship in part, scored two victories and finished eleventh overall in the GT4 championship. In 2009, Moore runner-up in the GT4 rating of the British GT Championship. He also appeared in four races of the GT4 European Cup and finished the season with a win from fourth place. 2009 Moore also debuted at the 24 Hours of Le Mans. With an age of 17 he became the youngest British participants, and until then the hitherto youngest LMP1 - starter in this race.
2010 Moore moved into formula racing and raced in the Formula Palmer Audi. Although he was not the pilot with three wins with the most wins, but with 12 podium finishes from 20 races he decided the league title before Maxime Jousse for themselves.
- 2007: British Ginetta Junior ( champion)
- 2008: British Ginetta G50 Cup (Master)
- 2008: British GT Championship, GT4 (11th )
- 2009: British GT Championship, GT4 (2nd place)
- 2009: GT4 European Cup (11th )
- 2010: Formula Palmer Audi