Born in Sackville Street, Dublin, on 10 June 1770, he was first educated at a preparatory school at Putney, whence he went for a short time to Harrow, and afterwards at the academy of Mr. Ralph at Castlebar, in the immediate neighbourhood of his home.

Trench matriculated at Trinity College, Dublin, on 2 July 1787, where his tutor was Matthew Young, afterwards bishop of Clonfert and Kilmacduagh, and graduated B.A.

Later in the same year (27 November) Trench was ordained deacon, and, having received priest's orders on 24 June 1792, he was in the same month inducted into the benefice of Creagh, in which his father's residence and the great fair town of Ballinasloe were situated.

In May 1834, on the death of James Verschoyle, the united sees of Killala and Achonry were, under the provisions of the Irish Church Temporalities Act, added to the charge of Trench.

From 1818 to his death Trench was president of the Irish Society; and it is evidence of his large-heartedness that the religious controversies in which his leadership of this movement involved no wise impaired the remarkable personal popularity which he enjoyed among his Roman Catholic neighbours.