Neary returned to the Archdiocese of Tuam in 1981, where he was appointed teacher at Holy Rosary College, Mountbellew, during which time he also served as curate in Moylough.

[1] The following year, Neary was appointed lecturer in sacred scripture at St Patrick's College, Maynooth, and subsequently professor of New Testament theology in 1991.

[6] In a statement on 21 May 2009, Neary described the Ryan Report as "sad and disturbing reading", and offered on behalf of the Catholic Church his unreserved apologies "for our failure to protect children".

"[10] On 6 October 2010, Neary, along with the Archbishops of Armagh, Cashel and Emly and Dublin, engaged in high-level talks with heads of Vatican congregations over the organisation of an apostolic visitation to Ireland, in the wake of the Murphy and Ryan reports.

[11] The report also stated that it is clear from the "excellent records" that a genuine effort was made to gather evidence from victims and their families during the Church inquiry stage and such "thoroughness is to be commended".

[12][13] On 12 March, he expressed "an urgent need for an enquiry to examine all aspects of life at the time, broadening the focus from one particular religious congregation, and instead addressing the roles and interrelationships between Church, State, local authorities and society generally", and hoped "that the Report of the Commission will enable that truth to surface in a clear and objective manner".

He went on to acknowledge and humbly ask "forgiveness for the abject failure of the Church for the pain and suffering visited on those women and their children in the Mother and Baby Homes nationally".

[17][18] In accordance with Canon law, Archbishop Neary submitted his episcopal resignation to the Dicastery for Bishops on his 75th birthday on 15 April 2021, but was expected to remain in the see until a successor was appointed.