A native of Bath, but Irish qualified thanks to his paternal grandfather, Burns made his debut for Gloucester as a 17-year-old. He then spent a loan period at Hartpury College before returning to help Gloucester to their 2014/15 European Challenge Cup success. After 101 appearances for Gloucester, Burns joined Ulster prior to the 2018/19 season where his dynamic play and creative kicking game immediately caught the attention of the Kingspan Stadium faithful and cemented his place in the squad.