Henry was appointed a Lord of the Bedchamber to George III in 1769, and advanced to the rank of General in 1782.
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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.
Claypole was appointed by his father-in-law one of the lords of his bed-chamber, clerk of the hanaper, and ranger of Whittlewood Forest) in Northamptonshire, where he built Wakefield Lodge, a magnificent house near Potterspury, (it came into the possession the Dukes of Grafton, the first duke having had a grant of the forest in 1685, with the title of hereditary ranger).
William Pulteney, Viscount Pulteney (1731–1763), his son, British MP for Old Sarum and Westminster, Lord of the Bedchamber