[1] He first played as a schoolboy in various juvenile competitions at Rossmore National School before later lining out as a student at Thurles CBS.
[4] Quirke scored two points from play when Clonoulty–Rossmore beat Nenagh Éire Óg in the 2018 Tipperary SHC final.
[12] He was later recalled to the senior panel and made his first appearance in a 2–14 to 0–18 defeat by Limerick in round 1 of the 2020 National League.
[13][14] Later that season, Quirke made his championship debut when he came on as a 73rd-minute substitute for Jason Forde in an All-Ireland qualifier defeat of Cork.
[16] On 5 August 2022, Quirke collapsed while playing a Tipperary SHC match for his club against Kilruane MacDonaghs at Semple Stadium.