Born the son of Edward John Power and Harriet Maud Power, Power joined the training ship HMS Britannia as a cadet in 1904 and, having won the King's medal as best cadet of his year, he was promoted to midshipman on 15 September 1905. He was promoted to acting sub-lieutenant on 15 January 1909 and to lieutenant on 15 April 1910 on his appointment to the battlecruiser HMS Indomitable in the Home Fleet. He became First Lieutenant in the destroyer HMS Nautilus in October 1912 and then attended HMS Excellent, the gunnery school at Portsmouth, in 1913. Power served as a gunnery officer throughout the First World War, initially in the battleship HMS Magnificent, then in the cruiser HMS Royal Arthur and next in the monitor HMS Raglan. In the Raglan he saw action in the Dardanelles Campaign, before transferring to the battlecruiser HMS Princess Royal in the Grand Fleet. He was promoted to lieutenant commander on 15 April 1918. After the war Power joined the directing staff at HMS Excellent. Promoted to commander on 31 December 1922, he became Assistant Director in the Naval Ordnance Department at the Admiralty in January 1923 and, after attending the Royal Naval Staff College, he became Executive Officer on HMS Hood, flagship of the battlecruiser squadron in the Atlantic Fleet in 1925. He joined the directing staff at the Royal Naval Staff College in 1927 and, having been promoted to captain on 30 July 1929, he joined the Ordnance Committee at the Royal Arsenal. He became Flag Captain of the Second Cruiser Squadron in the Home Fleet in the cruiser HMS Dorsetshire in April 1931 and, having served on the directing staff at the Imperial Defence College in 1933, he became commanding officer of the gunnery school HMS Excellent in October 1935. He was appointed a Commander of the Royal Victorian Order on 29 January 1936. He went on to be commanding officer of the aircraft carrier HMS Ark Royal in September 1937, and in that capacity, also became Flag Captain to the Flag Officer commanding aircraft carriers in the Home Fleet in July 1939.
Power served in the Second World War as assistant chief of the Naval Staff from May 1940 and was granted promotion to rear admiral on 25 June 1940. Appointed a Companion of the Order of the Bath on 1 July 1941, he became commander of the 15th Cruiser Squadron in the Mediterranean Fleet with his flag in the cruiser in August 1942. Appointed Flag Officer in charge of Malta in May 1943, he played a leading role in the planning for the Allied invasion of Sicily in July 1943, and, having been promoted to vice admiral on 4 August 1943, he led the planning for the Allied invasion of Italy and then commanded the naval forces for the actual landing of V Corps at Taranto in September 1943. Following the landings, he became head of the Allied military mission to the Italian government and was briefly Commander of the 1st Battle Squadron and second in command of the Mediterranean Fleet. Advanced to Knight Commander of the Order of the Bath on 1 January 1944, Power became commander of the 1st Battle Squadron and second in command of the Eastern Fleet with his flag in the battlecruiser in January 1944. He went on to be commander-in-chief of that fleet, renamed the East Indies Fleet, in November 1944, and conducted naval strikes on the Imperial Japanese Army in Borneo and Malaya. Flying his flag in Cleopatra, the first British ship to enter Singapore since the fall of that city over three years earlier, Power arrived in style to attend the final surrender of the Japanese there in September 1945.