He is the younger brother of Jessica Gleeson, the Republic of Ireland women's national team soccer player.
On 1 March 2015, he was selected at left wing-forward when WIT faced the University of Limerick in the Fitzgibbon Cup final.
On 5 October 2014, Gleeson lined out at centre-back when Mount Sion faced Ballygunner in the Waterford Senior Championship final.
[14] Gleeson made his Munster Championship debut on 25 May 2014 when he scored 1-02 from left wing-forward in a 1-21 apiece draw with Cork.
[15] On 3 May 2015, Gleeson was named at centre-back but played much of the game at right wing-back when Waterford faced Cork in the National League final.
[16] On 12 July 2015, Gleeson scored 0-02 from right wing-back when Waterford were beaten for the fourth time in six seasons by Tipperary in the Munster final.
A pulled quad hampered him during the early rounds of the National League while he also suffered an infected cut on his ankle.
Just before the start of the Munster Championship he sustained a hamstring injury after playing just 14 minutes of a club game with Mount Sion.
[25] On 31 March 2019, Gleeson was named at midfield but lined out at centre-forward when Waterford faced Limerick in the National League final.