Clifford's first post after ordination was as a teacher and Dean of Discipline in St Brendan's College, Killarney, where he taught from 1964 to 1972.

Clifford then studied Social Administration at the London School of Economics (1972–1974), where he was conferred with a master's degree with distinction.

On 12 September 1988 he was installed as Archbishop of Cashel and Emly in a ceremony in Thurles Cathedral, presided over by the late Cardinal Tomás Ó Fiaich.

In 1989 he became the first Kerryman to hold the office of Patron of the Gaelic Athletic Association, which brought immense satisfaction to the former footballers.

That same year he was awarded a PhD degree for a thesis on Carers of the Elderly and Handicapped at Loughborough University; this was based on studies he conducted in Kerry.

In October 2010, Archbishop Michael Neary of Tuam, along with Cardinal Seán Brady, Archbishops Diarmuid Martin of Dublin and Dermot Clifford of Cashel and Emly met for high-level talks with heads of Vatican congregations over the apostolic visitation of Irish dioceses in the wake of the Murphy and Ryan reports.