[3] Initially, Gleeson played for Northants on a match-by-match basis while continuing his full-time job coaching in schools and cricket clubs on behalf of the Lancashire Cricket Board, but in July 2016 he signed a three-year contract with Northants.

[4] He signed to play Twenty20 cricket for the Rangpur Riders in the 2016 Bangladesh Premier League.

[7] On 9 July 2020, Gleeson was included in England's 24-man squad to start training behind closed doors for the One Day International (ODI) series against Ireland,[8][9] and was later named as one of three reserve players in England's squad for the series.

[12] In July 2022, Gleeson was named in England's Twenty20 International (T20I) squad for their home series against India.

[13] He made his T20I debut on 9 July 2022, for England against India, taking the wickets of Rohit Sharma, Virat Kohli and Rishabh Pant, finishing with figures of 3/15.