Euan began his senior career with Hibernian in 2011 and was a key player in the club's Under 20 side before joining Kilmarnock in the summer of 2014. Prior to joining up at Killie, Euan had loan spells at Clyde and Arbroath. Euan signed for City at the beginning of the 2015-16 season. Consistent performances in midfield towards the end of the campaign led to him being offered a new contract at the Glebe although a serious injury saw him miss most of the successful 16-17 campaign. He returned to action for City towards the latter end of 2017.