Son of 2nd Baronet Simeon Stuart (d. 1761) and Elizabeth Dereham. Married (1761) to Anna Hook, daughter of sometime governor of Minorca, Lt-Col Hooke. Chamberlain of the Exchequer for life (1762-).1
Stuart ran an unsuccessful campaign against Henry Bilson Legge to become MP for Southampton in 1759, during which he was supported by the young Edward Gibbon and his father.2 He was later elected MP for Hampshire. In a journal entry, Gibbon wrote that "Sir Simeon is an old friend of ours, but take him out of fox-hunting and country affairs he has nothing left to recommend him but his good nature, which is really great".3
Boswell met Stuart at Lord Eglinton's in London on November 26, 1762, and described him as "much of a gentleman".