The 4th son of Montolieu Fox Oliphant-Murray, 1st Viscount Elibank, he entered the British Army in 1898, and was Aide-de-Camp to the Lieut-Governor of Bengal from 1900. He served in China in 1900 (medal); commanded Mounted Infantry Company, protecting the Sinho-Shanhaikwan Railway, 1901-1902. He was Aide-de-Camp to the General Officer Commanding the 1st Infantry Division, Delhi Manoeuvres, 1902. He served on the North-West Frontier, in India, and Chitral in 1903-1904.
He attended the Quebec Tercentenary Celebrations in 1908 (as a guest of Canadian Government) as representing his kinsman Gen. Hon. James Murray, 1st British Governor of Canada. He was Parliamentary Private Secretary to Sir Edward Grey, Secretary of State for Foreign Affairs from 1910-1914 and was a Member of the Special Mission to Foreign Courts to announce King George V's accession to the Throne in 1910.
Murray promoted a Bill through the House of Commons in 1914 to ameliorate the conditions of worn-out horse traffic. He served in World War I in France and Belgium from 1914-1916 with the 2nd King Edward's Horse, was mentioned in despatches and awarded the Distinguished Service Order in 1916. He was Assistant Military Attaché in Washington from 1917-1918, and was awarded the CMG in 1919.
Murray succeeded his brother in 1951 as Lord Elibank and Viscount Elibank. On his death, the title of Lord Elibank and the baronetcy passed to his kinsman James A. F. C. Erskine-Murray, the Viscountcy becoming extinct.