Conor played for Galway United FC's u19 squad during the 2014/15 season after joining from Mervue United. He also played a part in the friendly against a Liverpool XI in July 2015 and made his league debut shortly afterwards, away to St Patrick's Athletic on 31 July. He went on to make 9 league appearances for the club that year and also played in the EA Sports Cup Final, which Galway lost on penalties to St Pats.

In 2016 Conor made a further 17 league appearances for the Tribesmen and also scored his first league goal, in a 5-4 defeat to Wexford Youths at Ferrycarrig Park. In December 2017, Conor re-signed for Galway for the 2018 campaign. In December 2018, Conor re-signed with Galway once again for the 2019 season.