He was appointed Papal Nuncio to Ireland on 19 April 1969, shortly after the outbreak of the Troubles. This was a challenging time for the Church in Ireland then led by Cardinal William Conway as it adjusted to both the internal changes generated by the Second Vatican Council and the wider social changes. Alibrandi was ill-suited to coping with these changes and in particular the violence in Northern Ireland. It is widely assumed that he saw to it that the more overtly nationalist Tomas O'Fiaich was appointed to Armagh in 1977 after the death of Cardinal Conway. The journalist and author Ed Moloney in his book on the IRA asserts that Alibrandi's "sympathy for the IRA was a constant source of friction with the government in London." In many of the episcopal appointments made while Alibrandi was nuncio he favoured doctrinally 'sound', right of centre priests and in the case of the Archdiocese of Dublin picked two priests Kevin McNamara and Desmond Connell who were notably ill-suited. In a profile of the Archbishop at the time of his retirement T.P. O'Mahony observed in The Tablet "although he rarely gave interviews, and never overtly intervened in policy-making or in public controversies, it is beyond dispute that Archbishop Alibrandi wielded considerable influence behind the scenes." The respected academic and church historian Dermot Keogh assessing this period argues that "there was a general view that the best candidates had not been appointed...that a number were not up to the job, that most of the appointees shared a defensive attitude to matters of church and state. He had “a very testy relationship with three Taoisigh – Jack Lynch, Liam Cosgrave and Garret FitzGerald”. It was reported in September 2012 during the second Dr Garret FitzGerald Memorial Lecture at University College Cork by Seán Donlon, former secretary general at the Department of Foreign Affairs, that "It came to our attention that a substantial amount in three bank accounts in Dublin were way in excess of what was needed to run the nunciature. The source appeared to be South America." Donlon went on to say "Because of its size, we thought it appropriate to ask if the funds belonged to the Holy See." When contacted for an answer, Dr Alibrandi "quickly answered ‘no’ and that they belonged to ‘family’. When it was pointed out to him that the money was then liable under Irish taxation law to DIRT, he said he would retire shortly and the accounts would be closed".
