After his father died at the Siege of Derry, Steuart and his siblings were brought up by their uncle and aunt, who were wealthy and politically well connected.

Promoted to captain on 14 January 1709, he was given command of the fourth-rate HMS Greyhound during the War of the Spanish Succession.

[3] In 1726, acting as executor under his uncle's will, Steuart applied 5,000 Irish pounds to endow St George's School in Hanover Square.

He was elected member of parliament for Weymouth and Melcombe Regis in 1741 and while still in command of HMS Cumberland, he sailed for the West Indies early in 1742.

[6] With his flag in the second-rate HMS Duke, he became second-in-command of a fleet of 25 British and Dutch ships despatched under the command of Admiral Sir John Balchen to rescue a British squadron and convoy under Vice-Admiral Sir Charles Hardy, which had been trapped in the Tagus by a French Brest squadron: the British and Dutch fleet was successful in driving off the French, who retired in the face of the superior British and Dutch fleet without firing a shot, and Hardy's convoy was escorted safely to Gibraltar.