Alexander Gibson-Carmichael was born in Haddington, Peebleshire on 10 February 1895, the son of John Murray and Amy Kathleen Gibson-Carmichael (née Archdale). He joined the Royal Navy as a Cadet on 15 January 1908, was promoted to Midshipman on 15 September 1912 and appointed to the battleship HMS EXMOUTH on the same date. Alexander Gibson-Carmichael was appointed to the cruiser HMS PRINCESS on 14 November 1912 and was present at the Battle of the Heligoland Bight on 28 August 1914. He was promoted to Acting Sub Lieutenant on 15 September 1914, and, on 24 January 1915, was present at the Battle of the Dogger Bank.

On 13 June 1915 he was appointed to the battleship HMS AFRICA and, on 15 September 1915 he was appointed to HMS DOLPHIN ‘for Submarines‘. This was followed by an appointment to HMS C34 as First Lieutenant to date 3 November 1915. He was appointed to the HMS E16 as First Lieutenant to date 15 January 1916.

On 22 August 1916, during a patrol in the North Sea, HMS E16 was lost with all hands. A wreck, identified as E16, was discovered in 2001, sixteen miles off Heligoland and, from the damage to the wreck, it is believed that E16 either hit a mine or was torpedoed.

Alexander Gibson-Carmichael is commemorated on the Portsmouth Naval Memorial on Panel No. 20.