His usual position is back row forward.
Groves played for Cardiff RFC, Glamorgan Wanderers RFC and Cross Keys RFC.
He made his debut for Newport Gwent Dragons against the Ospreys 7 May 2010 as a second-half replacement.
Groves was offered a new contract by Newport Gwent Dragons in May 2014 but chose to move on.In the 2016-17 season, he joined Hong Kong Football Club (rugby section), playing in the Hong Kong Premiership.