Geary was born in 1709 to a family that resided at Aberystwyth in Ceredigion but that moved to England shortly after his birth.

[3] Before joining the navy, he was a noted bellringer, a member of the Ancient Society of College Youths, he participated in several early, record-breaking peals at St Bride's Church, Fleet Street, London.

[3] On her return to Britain Revenge was reassigned to sail with a fleet under Sir Charles Wager that was despatched to relieve Gibraltar.

[5] He quickly departed on a cruise in company with HMS Sunderland, and on 20 February the two ships came across the French frigate Elephant, capturing her after a short battle.

[7] He was then promoted to Commodore and appointed Commander-in-Chief of the squadron in the Medway, but relinquished the command in September that year.

[6] He was assigned to the 70-gun HMS Somerset, and sailed to North America with Admiral Edward Boscawen's fleet, returning in November.

[7] At the end of 1755 Geary received orders to join the Channel Squadron under Sir Edward Hawke.

[6] He sailed Resolution as part of the fleet under Hawke, quickly being assigned to command a squadron of ten ships of the line, two frigates and a fireship.

After a stay in port, he put to sea again on 30 April to intercept a French squadron assembling at Rochefort for a voyage to the East Indies.

He returned to Britain in October and became Port Admiral at Spithead, flying his flag aboard HMS Royal Sovereign.

[13] The death of Admiral Sir Charles Hardy in May 1780 led to Geary being recalled to service, despite being in poor health.

Geary put to sea, patrolling off Brest in the hope of preventing the joining of the French and Spanish fleets.