Parrey was commissioned lieutenant on 12 April 1761 and promoted commander on 11 May 1776, in which capacity he commanded the Bute tender in the Downs. Having joined the sloop Alderney 10 in February1777 following the death at Yarmouth of her commander, William Webster, he cruised the North Sea in search of enemy privateers and American vessels trading with the Netherlands.
He was posted captain with seniority from 2 May 1778 as a reward for participating in the King’s review of the fleet at Spithead that month, and he joined the Invincible 74 with the broad pennant of Commodore John Evans. This ship formed part of Vice-Admiral Hon. John Byron’s fleet which sailed for North America on 9 June, and after appalling weather had caused the force to disperse, the Invincible was towed into St. John’s, Newfoundland in great distress. At the end of October, she sailed from Newfoundland for England in the company of Vice-Admiral John Montagu’s flagship Europa 50 and a convoy of about one hundred vessels, but after separating in a gale on 7 November she eventually arrived at Spithead three weeks later under jury-masts with part of the convoy. On 25 January 1779 she was docked in Portsmouth to be refitted and coppered.
In May 1779 Parrey was appointed to the new Pandora 24, which at the time was undergoing copper sheathing at Deptford, and she was at the Nore towards the end of July before going around to Spithead in early August. Having then put back to the Downs, she set out for the coast of France with the Pegasus 28, Captain John Bazely, from which cruise the two vessels arrived at Spithead via the Downs on 9 September. Next being attached to the Grand Fleet, on 24 December the Pandora was dispatched with a small squadron under the orders of Captain John Jervis of the Foudroyant 80 which cruised off the Western Islands.
At the beginning of March 1780, the Pandora delivered a small convoy to the Downs from Portsmouth, and she was back at the latter port by the 12th. Towards the end of April, she ran down the Channel with the Halifax and Quebec convoy in the company of the Danae 32, Captain Samuel Graves, and having reached Torbay by 6 May they departed from that anchorage with forty-one sail on the last day of the month. On 5 June, being in a position about four hundred miles north-west of Cape Finisterre, the convoy was chased for some three hours in light winds by a French 74 and two other men-of-war, and at least two vessels were taken whilst many others scattered. A fog caused a further number of merchantmen to part company, and the Pandora and Danae continued their voyage with only about a dozen sail under their care. Arriving in North American waters, they captured the rebel privateers Jack on 18 July, and the Terrible on 2 September, but after departing Quebec on 25 October with the Danae and a homeward-bound convoy of thirty sail, the Pandora parted company in a gale at the mouth of the St. Lawrence on 7 November and arrived alone at Cork on 6 December. She then went around to Portsmouth in the early days of 1781 with part of the Quebec convoy and another which had arrived from the West Indies, and at the beginning of February she sailed for the Thames, whereupon Parrey left her.
He was next appointed to the Hannibal 50 on 28 March 1781, which at the time was refitting at Portsmouth, and on 4 May she left harbour for Spithead. At the end of the month, she sailed with the escort of the outward-bound East Indies, West Indies, Quebec and Newfoundland convoys, and having seen them safely out into the Atlantic she returned to Portsmouth to be docked.
In September 1781 Parry was appointed to the overhauled thirty-five-year-old Yarmouth 64, which given the publicly aired concerns over her vintage, firepower, and fitness for service in the line of battle was not a particularly desirable command. Victualled at Plymouth for foreign service, she departed for the Leeward Islands at the beginning of 1782 with Admiral Sir George Rodney’s force, and fought at the Battle of the Saintes on 12 April, suffering the substantial casualty figures of fourteen men killed and thirty-seven wounded. She later sailed to New York with the fleet under the command of Admiral Hugh Pigot before returning to the Leeward Islands at the end of the year. The Yarmouth eventually left the Caribbean with Rear-Admiral Sir Francis Samuel Drake’s squadron of half a dozen sail of the line in early 1783, and after parting company in heavy weather she arrived safely at Plymouth in May, whereupon Parrey left her.
Captain Parrey died at Kennington in Surrey on 11 July 1789.
The address in his will was given as Lambeth, Surrey.