The former Milton Keynes Dons midfielder and Republic of Ireland international joined Blues in June 2014 on a two-year contract.
Born in Dublin, Gleeson moved to England to join Wolverhampton Wanderers’ Academy set-up as a youngster.
He was given a three-year professional deal by Wolves in 2006. During that three year period with the Black Country outfit he spent several spells out on loan at clubs including Stockport County, Hereford United and Milton Keynes Dons, before signing with the Dons on a permanent basis in July 2009. He went on to make a total of 169 appearances for the Dons and scored 17 goals.
Gleeson made his Blues debut in the 2014/15 opening-day defeat at Middlesbrough and went on to make a total of 40 appearances in his first season at the club.