Following his ordination, Nulty served for ten years as a curate in the cathedral parish of Mullingar, as well as chaplain to the local Accord centre and spiritual director at St Finian's College.[3] He became the youngest parish priest in Ireland when he was appointed to St Mary’s parish, Drogheda, in August 1998.[4]
In light of the Government decision to hold a referendum on same-sex marriage in 2015, Nulty emphasised in November 2013 said while there is always a need to treat homosexuals with compassion, he added that the very nature of marriage and children and their importance to society are worth protecting, saying that "[the] Catholic Church will continue to hold that the differences between a man and woman are not accidental to marriage but fundamental to it and that children have a natural right to a mother and a father and that this is the best environment for them where possible".[11]
Ahead of a referendum on easing divorce restrictions in May 2019, he issued a statement suggesting that "the objective of the proposed referendum is not to support marriage, rather to liberalise divorce", and that "it is imperative that we continue to work together to promote marriage and family.”[12]
Following the easing of restrictions brought about by the COVID-19 pandemic, Nulty announced on 4 July that for the first time in living memory, a confirmation ceremony would take place in the open-air surroundings of a GAA stadium, with 392 primary school children from four parishes in Kilkenny city receiving the sacrament on 9 September in Nowlan Park, Kilkenny.[19][20] A similar ceremony took place for 361 primary school children from seven schools in Portlaoise on 18 September in O'Moore Park, Portlaoise.[21][22][23]
^"Our New Bishop"(PDF). Tullow, Grange & Ardattin Newsletter. 19 May 2013. Archived from the original(PDF) on 15 November 2018. Retrieved 24 September 2014.