Having passed his examination in 1762, Squire was commissioned lieutenant on 20 September 1765, seeing service off North America in the Mermaid 28, Captain James Smith. He was promoted commander of the Bonetta 10 on 21 January 1771 whilst still serving in North America, and this vessel was paid off in August 1772.
He recommissioned the sloop Otter 14 in January 1775, going out from Portsmouth to North America with money for the troops at Boston in March, and arriving in mid-April before cruising off the coast of Virginia from June. Whilst sailing for New York in early September, Squire survived the wrecking during a hurricane of one of the Otter’s tenders in the Back River near Langley, Virginia, north of Hampton. When sympathisers to the American cause burned the remains of the tender, took several prisoners and carried away her guns Squire demanded restitution in the local newspapers, but with his entreaties proving fruitless he landed with a party of men and ostentatiously hauled away two members of a printer’s family along with the printing press. The local authorities complained of his conduct to the Governor of Virginia, Lord Dunmore, who replied that he had witnessed the incident, and that Squire had acted in the interest of the residents by preventing the publication of seditious material.
On 26 October Squire led an attack up the James River on Hampton with several small craft manned by his own crew and local loyalists, but a number of sunken vessels in the channel delayed his access to the harbour. This allowed for the reinforcement of the local minutemen, and on the next day their expert rifle fire drove the assaulting force off. Remaining off Virginia, on 1 January 1776 the Otter under the orders of Captain Henry Bellew of the Liverpool 28, together with the Kingfisher 14, Commander Alexander Graeme, attacked the borough of Norfolk after the locals had refused supplies to the Navy. Ashore, Lord Dunmore ordered the burning of the waterfront houses from where American forces were firing on the ships, and a conflagration took hold that reportedly destroyed all but a dozen properties. Shortly afterwards, and being in company off Virginia with the Mercury 20, Captain James Montagu, the Otter took sixteen well-laden rebel vessels that were bound for St. Eustatius to barter for ammunition, the prizes being estimated at 40,000 guineas.
At the end of July 1776 the Otter transported over two dozen Virginian prisoners to St. Augustine in Florida, and after being sent to Antigua for a refit she returned to Vice-Admiral Lord Howe’s North American fleet in the summer of 1777. Here, in addition to taking a number of prizes, she was present in the Philadelphia Campaign from August-November. Squire retained the command of the Otter until the spring of 1778.
In June 1779 he was appointed to the Fortune 16 in home waters, in which he returned to Portsmouth at the end of October, and he was posted captain on 6 November to recommission the Ariadne 20 for service in the Downs. Unfortunately, having left Sheerness at the beginning of January to cruise off the German coast, she went aground two days later near Corton in Suffolk due to the incompetence of a pilot. After several perilous hours she was refloated with the assistance of boats from the shore and taken to Yarmouth, although the damage sustained was such that she was obliged to return to Sheerness for repairs.
On 30 April 1780 Squire was the senior officer of a squadron that gave chase to three French privateers of 20 to 24 guns off Flamborough Head. Regrettably only one of his consorts joined him in the pursuit, this being the armed ship Queen 20, Commander Richard Trotten, which sustained a great deal of damage, and the privateers were able to escape by taking to their sweeps. In July the Ariadne joined a small squadron under Commodore Hon. George Murray of the Cleopatra 32 which sailed north to the Shetlands to protect the incoming Greenland fishing fleet, and in May 1781 Squire assumed command of the Raleigh 32 in succession to Captain James Gambier. On the 29th of that month at a court-martial aboard the Santa Margarita 36 at the Nore under the presidency of Vice-Admiral Robert Roddam, he was honourably acquitted of failing to do his utmost to bring the French privateers to action on 30 April 1780, his conduct being described as ‘spirited, great, and highly to be recommended’ and that he was ‘acquitted of every aspersion thrown upon his conduct on that day’. The two commanders who failed to join battle, Commander Alexander Agnew of the Fury 16, and the elderly Commander Stephen Rains of the armed ship Loudoun 20, were sentenced to be broke following the court-martial.
In July 1781 Squire commissioned the new Cowes-built frigate Astraea 32, going out to Charleston from Portsmouth with a large convoy in October, and assisting the Diomede 44, Captain Thomas Lenox Frederick, and the Quebec 32, Captain Christopher Mason, in the capture of the American frigate South Carolina 40 off the Delaware on 20 December 1782 following an eighteen-hour pursuit. A further capture on 15 March 1783, in company with the Vestal 28, Captain William Fox, and Duc de Chartres 18, Captain John Child Purvis, was the privateer Julius Caesar. By the end of the year the Astraea was off New York to assist in the evacuation of the city following the cessation of hostilities, and she was paid off at the beginning of 1784.
Squire thereafter remained without employment until he joined the recommissioned Solebay 32 in November 1789, going out to the Leeward Islands in March 1790 and being paid off in the early autumn of 1791.
After a further period of unemployment he joined the recommissioned Magnificent 74 in June 1795, departing Chatham at the end of July for service in the North Sea and Channel, but being paid off after arriving at Spithead in January 1796 with her upper works in such ill-repair that she was taken into dock. He was appointed to the Atlas 98 in February 1797 upon the elevation to flag rank of Captain Edmund Dod, going out on a cruise with Rear-Admiral Sir Roger Curtis in the following month, and he was aboard her when the mutiny broke out at Plymouth on 26 April, his men immediately joining the insurrection but maintaining discipline, as illustrated when they ducked a woman for smuggling spirits on to the ship. The Atlas was back at sea by the middle of May to join the Channel fleet off Brest, and on 5 November she entered Plymouth with several other sail of the line before sailing later that month with a convoy for Jersey.
At the beginning of February 1798 the Atlas took up duty as the guard-ship at Portsmouth before sailing out with the Channel Fleet in April. On 13 May the fleet entered Torbay prior to returning to its station off Ushant at the beginning of June, and it was again in Torbay at the end of July from where the Atlas went around to Plymouth for a refit. She re-entered Plymouth from the Channel Fleet towards the end of October, and was at Portsmouth by the end of November. On 10 December her launch overset with the loss of the surgeon, but sixteen men were saved, including three personally by Captain Matthew Henry Scott of the Niger 32, after he had jumped into the water to haul them out. Squire continued to command the Atlas until January 1799 when he was succeeded by Captain Shuldham Peard on account of his poor health.
He was promoted rear-admiral on 14 February 1799, and died on 22 January 1800 at Durham Place, Chelsea, being buried at St. Luke’s Church, Chelsea.
Admiral Squire was a friend and early patron of Rear-Admiral Alexander Fraser.