After being ordained, Parry became rector of Hope, Flintshire in 1660; his brother Benjamin succeeded him in this post in 1666.
He was also appointed treasurer of Christ Church Cathedral, Dublin in 1661, prebendary of Bugthorpe, Yorkshire in 1662 and rector of St John of Jerusalem in the Diocese of Cork.
Many generations of the Parrys were buried in this tomb, which, having become defaced by time, was, on the repair of the Church in 1848, surmounted with an inscribed white marble slab at the expense of Dr. John Parry's representatives, Dame Emma Elizabeth Puleston of Albrighton Hall, Shropshire, relict of Sir Richard Puleston, Bart., Anna Eleanora, Frances and Elizabeth Hawkshaw, daughters of Lieutenant Colonel John Stuart Hawshaw of Divernagh, County Armagh.
Edward Parry, D.D., Pro-Vice-Chancellor of the University of Trinity College, Dublin, was consecrated Bishop of Killaloe, 28th March, 1647, and died of the plague in this city, July 20th, 1650.
Dame Emma Elizabeth Puleston of Albrighton Hall, Shrophire relict of Sir Richard Puleston Bart and Anna, Eleanora, Frances, and Elizabeth Hawkshaw, daughters of the late Lieut Colene John Stewart Hawkshaw of Divernagh Co. Armach, caused this new monument to be erected in memory of the above named bishops.