Leeper was born 4 January 1887 in Melbourne, Australia. He was the son of Alexander Leeper, Warden of Trinity College, Melbourne and Adeline, the daughter of Sir George Wigram Allen. In 1912 he was the Second Class Assistant in the Egyptian and Assyrian Department of the British Museum. 1915-18 he was seconded to the Department of Information and Foreign Office. 1918-20 he served on the British Delegation at the Paris Peace Conference. He became Second Secretary in the Foreign Office in 1920. Leeper was then Assistant Private Secretary to Lord Curzon of Kedleston, 1920-24. In 1922 he served on the British Delegation at the Lausanne Peace Conference. In 1924 he was promoted to First Secretary in the Foreign Office and was seconded to work on the setting up of an Australian Foreign Service in Melbourne. He was the First Secretary at H.M. Legation at Vienna, 1924-28, and in 1928 transferred to the Western Department at the Foreign Office. In 1933 he was promoted to Counsellor. Leeper died 24 January 1935.