Drake, in command of HMS Mercury, was one of Commodore George Brydges Rodney's senior officers and was sent into Conception and Trinity Bay's and as far north as Cape Bonavista where he had authority to hear appeals from decisions of fishing admirals and to enforce the various provisions of King William's Act of 1699.
In 1750 at the age of 26, Drake served as the de facto Governor of Newfoundland under Commodore Rodney, senior naval officer in 1750 and 1751, and was promoted to the full position in 1752.
Drake was instrumental in making reforms in the Newfoundland justice system in the way that prisoners were incarcerated and the requirement that people charged with criminal offences had to be transported to England for trial. The instructions given to Drake were to appoint judges and commissioners oyer and terminer to hear all criminal cases except treason. After returning to England Drake had suggested additional reforms urging that the provision forbidding the execution of those convicted of criminal offences be changed. He suggested that a secure prison be built in St. John’s as prisoners could easily escape or freeze to death while awaiting transport to England while incarcerated over the winter while the British cabinet determined their fate. Changes were granted including the right to execute prisoners found guilty of crimes.
Drake saw action in the West Indies during the Seven Years' War, also at The Downs and at Portsmouth, and saw action during the American Revolutionary War. He was promoted Rear-Admiral of the Blue in 1778 and Rear-Admiral of the Red in 1779, Vice-Admiral of the Blue in 1780 and appointed to command a squadron of the Channel fleet under Vice-Admiral George Darby. Severe attacks of gout limited his ability to command, however, and terminated his active career abruptly that year; he was nevertheless promoted Vice-Admiral of the Red in September 1787.
On January 23, 1788 in Ripley he was married by special licence, because she was a minor, to the only daughter of George Onslow, for many years the member of parliament for Guildford. From that relationship Drake fathered a son, Francis Henry Drake. Francis Henry in 1794 claimed succession to his uncle in the baronetcy but was unsuccessful because of doubts raised of his parents’ marriage.