He married but died without male issue at a relatively early age and was succeeded by his half-brother, George, the 3rd Baronet, who settled in Ireland and was High Sheriff for cos. Armagh and Tyrone.

His son, the sixth Baronet, represented Dublin University and Enniskillen in the Irish House of Commons.

Lord Gosford married Mary, daughter of Robert Sparrow of Worlingham Hall in Suffolk.

In 1835 he was created Baron Worlingham, of Beccles in the County of Suffolk,[5] in the Peerage of the United Kingdom, which gave him and his descendants an automatic seat in the House of Lords.

[6][7] His son, the fourth Earl, served as Lord-Lieutenant of County Armagh and was also a Lord of the Bedchamber to the Prince of Wales and Vice-Chamberlain of the Household to Her Majesty Queen Alexandra.

The heir presumptive is the present holder's first cousin Nicholas Hope Carter Acheson (born 1947).