Died 1807. He was descended from a long-established Renfrewshire family and was the son of Thomas Brisbane and of his wife, Isabel Nicholson.
Brisbane was commissioned lieutenant on 5 August 1757 and apparently passing through the rank of commander was posted captain on 24 September 1761 with his appointment to the Nightingale 20, which he commanded off North America and in the Leeward Islands. In April 1762 he was appointed to the ex-French corvette Echo 24, and he served in the West Indies until the end of the Seven Years War, assisting the Alarm 32, Captain James Alms, in the capture from the Spanish of the storeship Fénix 18 on 28 May, and the Thetis 22 on 3 June.
During 1769-1770 he commanded the Cruizer 8 in home waters, leaving her in the autumn of the latter year to join the Cerberus 28, which he had in the Channel and home waters for the best part of the next three years.
In December 1775 Brisbane recommissioned the Flora 32, which he took out to North American with a convoy in the following April. On 8 July 1777 his command assisted the Rainbow 44, Captain Sir George Collier at the recapture of the British frigate Fox 28 and the capture of the American frigate Hancock 34. He was the senior naval officer at Rhode Island when the French fleet arrived in August 1778, obliging him to destroy the Flora, four other frigates, and two sloops, to prevent them falling into enemy hands. He then remained at Rhode Island as senior officer assisting the Army in manning the batteries against the French and the rebel army.
Having commissioned the new Alcide 74 during the previous autumn, he fought at the Moonlight Battle off St. Vincent on 16 January 1780 where his main-topmast was shot away by the Monarca 70. Subsequently when the fleet reached Gibraltar the Alcide had to be towed away from the Spanish batteries. After being coppered at Plymouth the Alcide sailed for the West Indies in June but Brisbane vacated the command soon afterwards, arriving home with Admiral Sir George Rodney’s despatches in December. During the summer of 1781 he recommissioned the Hercules 74 in home waters, but he was obliged to leave her in December as his poor health prevented him from taking her to the West Indies.
Brisbane was not thereafter employed, but in accordance with seniority he was promoted rear-admiral on 21 September 1790, vice-admiral on 12 April 1794, and admiral on 14 February 1799. He died at Southampton on 10 December 1807.
Brisbane married Mary, a daughter of Admiral James Young, on 11 June 1759 at Stonehouse, Devon and had five sons: Commander John Douglas Brisbane who drowned on one of the prizes from the Battle of the Saintes in 1782; Lieutenant-Colonel Thomas Stewart Brisbane who was killed on San Domingo in 1795; Commander William Henry Brisbane of the Navy who died in 1796 having been poisoned by French prisoners at Gibraltar; Rear-Admiral Sir Charles Brisbane, and Commodore Sir James Brisbane. He also had six daughters, one of whom married Captain Sir Charles Douglas.