Drake was appointed to command the 70-gun in 1766, and moved from there to the 74-gun HMS Torbay between 1772 and 1775. Torbay was the guardship at Plymouth during this time. With the outbreak of the American War of Independence, Drake was appointed to command the 74-gun in the spring of 1778. The Russell was one of the squadron which sailed for America under the command of Vice-Admiral John Byron. The Russell was badly damaged in a gale which scattered the squadron, and Drake was forced to return to England for repairs. He therefore did not sail to America until the spring of 1779. During that year and the early part of 1780, Drake operated as part of the fleet under the command of Vice-Admiral Mariot Arbuthnot. Drake was then sent to join Rodney in the West Indies, and accompanied him to the coast of North America, and back again to the West Indies, where he received a commission as rear-admiral, dated 26 September 1780. He then hoisted his flag in the 70-gun ; took part under Rodney in the operations against the Dutch Islands, including the Capture of Sint Eustatius, and was detached under Sir Samuel Hood to blockade Martinique, where, with his flag in, he was warmly engaged in the Battle of Fort Royal against with De Grasse on 29 April 1781. In August, with his flag again in the Princessa, he accompanied Hood to North America, and commanded the van at the Battle of the Chesapeake on 5 September, with the fleet under Sir Thomas Graves. The Princessa was heavily damaged in the battle, forcing Drake to shift his flag temporarily to the 74-gun. He afterwards returned with Hood to the West Indies, took part with him in the Battle of Saint Kitts in January 1782, and on 12 April, by the accident of position, commanded the vanguard of the fleet under Sir George Rodney in the Battle of the Saintes. He was made a baronet on 28 May 1782 for his conduct on this occasion. He continued in the West Indies until the end of the war, after which he had no further service.
Later life
On 12 August 1789 was appointed a junior lord of the admiralty, but died shortly afterwards, on 19 October 1789. He was twice married, first, to Elizabeth Hayman, of Kent; and, secondly, in January 1788, to Pooley, daughter of George Onslow, Esq., M.P. for Guildford, but left no issue, and the baronetcy became extinct. His elder brother, Francis William, a vice-admiral, with whom he is frequently confused, died about the same time, with descendants by his daughter but no male issue; and the eldest brother, Francis Henry, the hereditary baronet, dying also without issue this title too became extinct.