Born in Portaferry, County Down, Conlan attended St Columba's School in the town and played for junior clubs Grosvenor Youth and Portaferry.[3] He was recruited by Championship side Burnley in the summer of 2011, signing a two-year scholarship with the club.[4] He was a key member of the youth side that reached the 2011–12 FA Youth Cup semi-finals, eventually losing 3–1 to Blackburn Rovers on aggregate.[3]
In March 2012, whilst still a first-year apprentice, Conlan signed his first professional contract in a two-year deal.[5] He remained a regular in the youth and reserve sides until he suffered a knee injury, and in April 2014 it was announced by Burnley that he would not be retained at the end of the season when his contract expired.[3] However, he continued to train with the club during pre-season and in September 2014, after recovering from injury, he signed a one-year contract extension with the club.[6] In April 2015, it was announced that Conlan had signed another one-year contract extension until the summer of 2016.[7]
In June 2019 he signed a new contract with Morecambe.[14] He scored his first professional goal for Morecambe when he scored in an EFL Trophy tie against Carlisle United on 12 November 2019.[15]