At 18, he won the lead role of Oskar in the National Theatre of Scotland's production of Let The Right One In, adapted for the stage by Jack Thorne and directed by John Tiffany. The play opened at Dundee Rep in the summer of 2013 before transferring to the Royal Court Theatre in London the following December and then onto the Apollo Theatre in the West End in 2014, with Quinn reprising the lead role on both occasions. He then attended Guildhall School of Music and Drama. Since graduating he has performed in London's National Theatre and Old Vic as well as various Scottish theaters including a national tour of "Oor Wullie"- The Musical, where he played the titular role.