HMS Indefatigable was one of the Ardent-class 64-gun third-rate ships-of-the-line designed by Sir Thomas Slade in 1761 for the Royal Navy. She was built as a ship-of-the-line, but most of her active service took place after her conversion to a 44-gun razee frigate. She had a long career under several distinguished commanders, serving throughout the French Revolutionary Wars and the Napoleonic Wars. She took some 27 prizes, alone or in company, and the Admiralty authorised the issue of four clasps to the Naval General Service Medal in 1847 to any surviving members of her crews from the respective actions. She was broken up in 1816.

Indefatigable was ordered on 3 August 1780 (long after Slade's death), and her keel was laid down in May 1781 at the Bucklers Hard shipyard in Hampshire owned by Henry Adams. She was launched in early July 1784 and completed from 11 July to 13 September of that year at Portsmouth Dockyard as a 64-gun two-decked third rate for the Royal Navy. She had cost £25,210 4s 5d to build; her total initial cost including fitting out and coppering was £36,154 18s 7d. By that time, she was already anachronistic for the role of a ship of the line as the French only built the more powerful 74-gun ships, and was never commissioned in that role.

In 1794, she was razéed; her upper gun deck was cut away to convert her into a large and heavily armed frigate. The original intention was to retain her twenty-six 24-pounder guns on her gundeck, and to mount eight 12-pounder guns on her quarterdeck and a further four on her forecastle, which would have rated her as a 38-gun vessel. However, it was at this time that the carronade was becoming more popular in the Navy, and her intended armament was altered on 5 December 1794 with the addition of four 42-pounder carronades to go on her quarterdeck and two on her forecastle. Indefatigable was thereafter rated as a 44-gun fifth-rate frigate, along with Magnanime and Anson, which were converted at about the same time. The work was carried out at Portsmouth from September 1794 to February 1795 at a cost of £8,764. On 17 February 1795, a further two 12-pounder guns were added to her quarterdeck, though her official rating remained unchanged.

Indefatigable was first commissioned in December 1794 under Captain Sir Edward Pellew. He commanded her until early 1799.

On 9 March 1795, Indefatigable, Concorde, and Jason captured numerous French prizes: Temeraire, Minerve, Gentille, Regeneration, and a brig and sloop of unknown names. In October, the Dutch East Indiaman Zeelilee was wrecked in the Isles of Scilly with the loss of 25 of her 70 crew. Indefatigable rescued the survivors.

On 20 March 1796, Indefatigable and her squadron chased three French corvettes, of which the Volage of 26 guns ran ashore under a battery at the mouth of the Loire. Volage lost her masts in running ashore, but the French were later able to refloat her. Her two consorts Sagesse and Eclatant escaped into the river. In this action, Amazon had four men wounded.

Between 11 and 21 March Indefatigable's squadron captured the vessels Favorite Sultana, Friends, Providence, Four Marys, Aimable Justine, and Nouvelle Union. They also destroyed two unnamed brigs and a chasse maree. The vessels sharing in the prize money were: Indefatigable, Concorde, Révolutionnaire, Amazon, Argo, and the hired armed cutter Dolly and hired armed lugger Duke of York.

On 13 April 1796, Indefatigable was in pursuit of a French frigate. Pellew signalled to Révolutionnaire to cut her off from the shore. Révolutionnaire then captured the French frigate Unité after having fired two broadsides into her. Unité had nine men killed and 11 wounded; Révolutionnaire had no casualties. The Royal Navy took the frigate into service as HMS Unite.