Adam was the second son of Alexander Duncan of Lundie, Forfarshire, (d. May 1777) Provost of Dundee, and his wife (and first cousin once removed) Helen, daughter of John Haldane of Gleneagles, was born at Lundie. In 1746, after receiving his education in Dundee, he entered the Royal Navy on board the sloop Trial, under the care of his maternal uncle, Captain Robert Haldane, with whom, in HMS Trial and afterwards in HMS Shoreham, he continued till the peace in 1748. In 1749 he was appointed to HMS Centurion, then commissioned for service in the Mediterranean, by the Hon. Augustus Keppel (afterwards Viscount Keppel), with whom he was afterwards in HMS Norwich on the coast of North America, and was confirmed in the rank of lieutenant on 10 January 1755.[1]

In August 1755 he followed Keppel to the Swiftsure, and in January 1756 to the Torbay, in which he continued till his promotion to commander's rank on 21 September 1759, and during this time was present in the expedition to Basque Roads in 1757, at the reduction of Gorée in 1758, and in the blockade of Brest in 1759, up to within two months of the battle of Quiberon Bay, from which his promotion just excluded him.[1]

From October 1759 to April 1760 he had command of the Royal Exchange, a hired vessel employed in petty convoy service with a miscellaneous ship's company, consisting to a large extent of boys and foreigners, many of whom (he reported) could not speak English, and all impressed with the idea that as they had been engaged by the merchants from whom the ship was hired they were not subject to naval discipline. It would seem that a misunderstanding with the merchants on this point was the cause of the ship's being put out of commission after a few months.[1]

As a commander Duncan had no further service, but on 25 February 1761 he was posted and appointed to the HMS Valiant, fitting for Keppel's broad pennant. In her he had an important share in the reduction of Belle Île in June 1761, and of Havana in August 1762. He returned to England in 1763, and, notwithstanding his repeated request, had no further employment for many years.[1]

During this time he lived principally at Dundee, and married on 6 June 1777 Henrietta, daughter of Robert Dundas of Arniston, Lord President of the Court of Session. It would seem that his alliance with this influential family obtained him the employment which he had been vainly seeking during fifteen years. Towards the end of 1778 he was appointed to HMS Suffolk, from which he was almost immediately moved into HMS Monarch. In January 1779 he sat as a member of the court-martial of Keppel, and in the course of the trial interfered several times to stop the prosecutor in irrelevant and in leading questions, or in perversions of answers. The admiralty was therefore desirous that he should not sit on the court-martial of Sir Hugh Palliser, which followed in April, and the day before the assembling of the court sent down orders for the Monarch to go to St. Helens. Her crew, however, refused to weigh the anchor until they were paid their advance; and as this could not be done in time, the Monarch was still in Portsmouth harbour when the signal for the court-martial was made[2]; so that, sorely against the wishes of the admiralty, Duncan sat on this court-martial also.[1]

During the summer of 1779 the Monarch was attached to the Channel fleet under Sir Charles Hardy; in December was one of the squadron with which Rodney sailed for the relief of Gibraltar, and had a prominent share in the action off St. Vincent on 16 January 1780. On returning to England Duncan quit the Monarch, and had no further command till after the change of Ministry in March 1782, when Keppel became first lord of the admiralty. He was then appointed to HMS Blenheim of 90 guns, and commanded her during the year in the Grand Fleet under Howe, at the relief of Gibraltar in October, and the rencounter with the allied fleet off Cape Spartel. He afterwards succeeded Sir John Jervis in command of the Foudroyant, and after the peace commanded HMS Edgar as guardship at Portsmouth for three years. He attained flag rank on 24 September 1787, became Vice Admiral 1 February 1793, and Rear Admiral 1 June 1795. In February 1795 he was appointed commander-in-chief in the North Sea, and hoisted his flag on board HMS Venerable