The Cork born player, aged 22, started his career at Avondale United before signing for Scottish Premier League side Celtic in 2012. Kelleher would move through the under 17 and under 20 team during his time with The Bhoys before making his way into the full set up in 2016.
However, Fiacre was moved out on loan to Peterhead, who were then competing in Scottish League 1 and went on to make 25 appearances in all competitions, scoring 3 goals in the process.
In June 2017, Kelleher made the move south to English Football League side Oxford United, where he signed on a two year deal. Solihull Moors went on to sign the Republic of Ireland defender in August 2017 and went on to make 38 appearances in the Vanarama National League, netting on 2 occasions.
In June 2018, Kelleher signed for The Silkmen on a season-long loan.