He was installed as Dean of Cork on 4 November 1667, and made Bishop of Limerick, Ardfert and Aghadoe in 1672. In 1678 he became Archbishop of Tuam, and in 1712 and 1714 he served as one of the Lords Justices of Ireland. Sir Thomas Vesey, 1st Baronet, ancestor of the Viscounts de Vesci
Agmondisham Vesey, ancestor of the Earls of Lucan
John Vesey, Archdeacon of Kilfenora, ancestor of the Barons Fitzgerald and Vesey
Mary, married to Sir Robert Staples, 4th Baronet
Elizabeth, married to Richard Dawson, ancestor of the Earls of Dartrey
Anne, married to Henry Bingham, ancestor of the Barons Clanmorris.