[3] Drennan studied at Maynooth seminary, earning BA(NUI) and the Biblical Institute, Rome, and was ordained to the priesthood on 16 July 1968 for the Diocese of Ossory.

When he returned to Ireland he was appointed to the Faculty of Theology in Maynooth College (1985–97) rising to the position of Professor of Old Testament.

The principal consecrator was Cardinal Desmond Connell; his co-consecrators were Archbishop Luciano Storero, the Apostolic Nuncio to Ireland, and Laurence Forristal, the Bishop of Ossory.

[1] In November 2009, there were several calls for Bishop Drennan to resign from his post for his inclusion as part of the Murphy Report, surrounding a sexual abuse scandal in the Dublin archdiocese.

"[6] The report's assessment was that the Archdiocese acted correctly in addressing the issue that relates to Dr. Drennan given the fact that the civil authorities brought no charges against the priest in question.