Hope was born at South Queensferry, West Lothian in Scotland. He was the eldest son of the 6th Earl of Hopetoun. He was educated at Eton College and the Royal Military Academy Sandhurst, where he passed in 1879 but did not join the Army. He looked after the family houses and lands. In 1883 he became active in the House of Lords. He served as a Lord in Waiting from June 1885 to January 1886 and August 1886 to August 1889.