His older brother Cian Kelleher is a fellow professional rugby union player.

[3] He scored both tries as Leinster A beat the Scarlets Premiership Select side 15–8 to win the final of the inaugural Celtic Cup in 2018.

Kelleher received his first call up to the senior Ireland squad on 15 January 2020 for the 2020 Six Nations Championship.

[9] Kelleher joined the 2021 British & Irish Lions pre tour training camp in Jersey, as informal cover for hooker due to the unavailability of touring hookers Jamie George and Luke Cowan-Dickie.

Kelleher was not added to the touring party at the time,[10][11] but was called up to the Lions squad in South Africa on 15 July.