A sinecure is a job that provides income without requiring much if any work, and they were a common source of income for the upper classes in the past. Usually, someone else was hired to do any necessary work at a much lower income.
Groom of Stole and Mistress of Robes
Hamilton had £500 as Groom of Stole and £400 as Mistress of Robes and possibly also £400 as Lady of Bedchamber. Middlesex was apparently only Mistress of Robes.
Hamilton, Lady Jane WS 12 July 1736 (Add. MS 24397 f. 90v). Res. offices of Groom of Stole and Mistress of Robes by 6 June 1745 when granted pension of £1200
Middlesex, Grace Countess of WS as Mistress of Robes 24 June 1747
900 pounds a year was a lot of money back then.