Thompstone was signed by the London Irish Academy. His debut first-team start was against Worcester Warriors in the EDF Energy Cup in 2008. A serious ankle injury in October 2009 kept him out of the side until January 2011.
Thompstone signed with Leicester Tigers for the 2012-2013 season.
Thompstone ended his first season with the Tigers as their top try scorer with 9 in all competitions, including a hat trick on his Premiership debut for the club He made 22 appearances the following season, scoring 4 tries.
Thompstone made 22 appearances in the 2014/15 season, scoring 5 tries for the club He started the 2015/16 season making 10 consecutive starts.