Corry is the son of Edward Corry, sometime Member of Parliament, and Catharine Bristow. His cousin is the writer Catherine Dorothea Burdett. He is educated at the Royal School, Armagh, where his contemporaries include Robert Stewart, Viscount Castlereagh, and later at Trinity College, Dublin, from which he graduates in 1773. On October 18, 1771 he is admitted to the Middle Temple and called to the bar at King’s Inns in 1779.
Corry succeeds his father as Member of Parliament for Newry in 1776, sitting in the Irish House of Commons until the Acts of Union 1800. From 1782 to 1789 he serves as equerry to Prince Henry, Duke of Cumberland, being described in 1794 by Rt. Hon. Sylvester Douglas as “a well-bred man…He has no brogue…He once acted as a sort of groom of the bedchamber to the late Duke of Cumberland.” In 1798, he is also elected for Randalstown, but chooses not to sit and, in 1802, he is returned to the British House of Commons for Newry. He serves as a Whig at Westminster until 1806. It is written in 1783 that he would expect to enter high office, given that “he lives expensively and does not pursue his profession, which is the law.” In 1788 he becomes Clerk of the Irish Board of Ordnance. The following year he is appointed a commissioner of the revenue. Finally in 1799 he is appointed Chancellor of the Exchequer of Ireland and a Lord High Treasurer of Ireland in place of Sir John Parnell, who quarreled violently with William Pitt the Younger over the projected union, which he categorically refuses to support. In 1795 he becomes a Privy Councillor.
In 1802 Corry is dismissed from the Exchequer and replaced by John Foster (later Lord Oriel), he is awarded, however, £2,000 p.a. in compensation. In 1806 the changes in ownership of the Newry estates alters his position. The lands pass to a senior line of the Needham family and they support General Francis Needham, 1st Earl of Kilmorey, at the general election. Corry does not have the funds needed, in excess of £5000, to purchase a seat elsewhere. However, Lady Downshire is inclined to support the Grenville ministry and comes to a formal agreement with Corry to give him £1000 towards his expenses should he be successful in Newry, and, if not, to bring him in for another borough. He fails against the Needham interest in Newry, but a seat at Newport, Isle of Wight, is purchased for him, with £4000 from Lady Downshire, and he is appointed to the Board of Trade. Six months later Grenville’s ministry has fallen and there is another general election. Corry stands, again unsuccessfully, for Newry.
Corry is unmarried but has a long-term relationship with Jane Symms. They have three sons and three daughters. His daughter Ann marries Lt. Col. Henry Westenra, the brother of Robert Cuninghame, 1st Baron Rossmore. His residence in Newry is the Abbey Yard, now a school, and Derrymore House, Bessbrook, County Armagh, which he had inherited from his father and sold in 1810. It is now the property of the National Trust. During his life, a road is constructed from near the main entrance of Derrymore House around Newry and links up with the Dublin Road on the southern side of the town primarily for his use. This road subsequently becomes known as “The Chancellor’s Road,” as a result of his term as the Irish Chancellor of the Exchequer. A local legend has it that the road is constructed after an incident in which Corry’s stagecoach is stoned while passing through Newry by people angry at an unpopular window tax he had introduced. The road has retained this name but it is cut in half by the Newry by-pass in the mid-1990s, however, as a result of works associated with the new A1 dual carriageway, the two-halves of the road are now reconnected.