Having graduated from the Naval Academy at Portsmouth, Harmood was commissioned lieutenant on 19 February 1759 and appointed to the Aquilon 28, Captain Chaloner Ogle. In 1771 he became the first lieutenant of the Arethusa 32, Captain Andrew Snape Hamond, in which frigate he served in home waters and in North America, prior to being appointed third lieutenant of Vice-Admiral Lord Howe s flagship Eagle 64, Captain Henry Duncan, on the North American station in 1776.
He was promoted commander of the sloop Falcon 14 at New York on 16 February 1777 and during the summer cruised successfully off Newport, capturing the privateers Mehitabel and General Arnold in a boat attack at Sandford, Connecticut on 24 June 1778. On 7 August 1778 the Falcon was sunk at Rhode Island to both prevent capture by the French fleet and to act as a block ship to prevent their landing, although she was later salvaged and recommissioned.
Harmood was posted captain on 17 October 1778, joining the Conqueror 74 with the broad pennant of Commodore Thomas Graves and sailing to the Leeward Islands in December with Vice-Admiral Hon. John Byron s fleet. Flying the flag of Rear-Admiral Hyde Parker, he commanded the Conqueror at the Battle of Grenada on 6 July 1779 but his was one of the few ships not to suffer any casualties as she saw barely any action because of Byron s poor tactics. Upon Parker s elevation to the position of commander in chief following the return home of Byron and the wounded Vice-Admiral Hon. Samuel Barrington he transferred with the admiral to the Princess Royal 90 in August. He commanded this vessel at the Battle of Martinique on 17 April 1780, losing five men killed and fourteen wounded, and remained in the Leeward Islands for the remainder of the May-July campaign, although his ship did not suffer any casualties during the fleet skirmishes in the former month.
Returning to Europe in July aboard the Medway 60 with Parker s flag following that officer s fall-out with Admiral Sir George Rodney, Harmood commanded the Cumberland 74 in an acting capacity for Captain Joseph Peyton in the Channel fleet campaign that autumn. After recommissioning the Medway 60 in January 1781 he commanded her at the relief of Gibraltar on 12 April, in the Channel fleet campaign of June-November, and in Rear-Admiral Richard Kempenfelt s brilliant attack on the Comte de Guichen s convoy on 12 December. A day later he took the privateer G n reuse, and he left the Medway during the following year..
In March 1783 he was appointed to commission the new Ardent 64, commanding her as a guardship at Portsmouth until she was paid off in March 1786, and during the Russian Armament of 1791 he served as a regulating captain.
Harmood became an extra commissioner in December 1793 which role entitled him to a handsome salary, whilst also serving as the commissioner at Gibraltar and Malta. On 25 June 1796 he became a commissioner without special function, and in the same year assumed the role of commissioner at Sheerness. He was commissioner at Chatham from 1801-6, and became a director of Greenwich Hospital.
Harmood died at his residence in Grosvenor Square, London in the early part of 1809.
He was married in 1782 and had issue a son and a daughter.