Carnegie, a younger son of the 6th Earl of Northesk, entered the Navy in 1771 and became a captain in 1782. From 1788, after the death of his elder brothers, he was styled Lord Rosehill and succeeded to the earldom in 1792. As captain of the 'Monmouth' during the Nore mutiny of 1797 he was sent by their committee of delegates as an emissary to the king but, their requests being denied by message, did not return in person to his ship as they had demanded. In 1803 he was appointed to the 'Britannia', initially under Cornwallis but remained in her when he became a rear-admiral in April 1804 and was sent to reinforce Calder off Cadiz in August 1805. 'Britannia' thus came under Nelson's command on his return to that station and was fourth or possibly sixth (reports differ) in his weather line at Trafalgar on 21 October 1805, where Carnegie's seniority also made him the often-forgotten third-in-command, after Collingwood. He was criticized for being slow into action, probably unfairly since 'Britannia’ was old, notoriously slow and long out of dock, but she saw close fighting with 52 killed. He also did sterling work in the storm that followed, taking crews off prizes ordered to be destroyed. For his services he was made a Knight of the Bath and also received the flag officer's gold medal, of which Collingwood's is the only other from Trafalgar, since Nelson's was stolen in 1900. He stayed ashore from 1806 but rose by seniority to Admiral of the White and Rear-Admiral of Great Britain in 1821. From 1827 to 1830 he was commander-in-chief at Plymouth and on his death was buried with Nelson and Collingwood in St Paul's Cathedral.