As captain of the frigate Melampus, he took part in the Battle of Tory Island in October 1798, capturing the Résolue two days later, during the French Revolutionary Wars.

He was promoted to lieutenant on 8 March 1782 to serve aboard Crown, taking part in the relief of Gibraltar under Lord Howe, and the subsequent battle of Cape Spartel in October.

During the peace he travelled through France, but was recalled to serve aboard Perseus, Dido, and then Adamant, the flagship of Sir Richard Hughes on the North American Station.

[1] Moore was promoted to post-captain on 2 April 1794, soon after the start of the Revolutionary War, with command of the 32-gun frigate Syren,[2] in the North Sea and the coast of France.

In 1808, he served as commodore, flying his broad pennant in the new ship Marlborough[1] assisting Admiral Sir Sidney Smith with the Portuguese royal family's escape to Brazil,[1] and was subsequently made a Knight of the Order of the Tower and Sword.

[2] Moore commanded Chatham from March 1812, until promoted to rear-admiral on 12 August 1812,[2][3] and served as Commander-in-Chief in the Baltic for a short time, flying his flag in HMS Fame.