Born the son of Frederick William Stanhope and Shiela Mary Hattemore (née Cutler), Stanhope was educated at the London Nautical School, Worthing High School for Boys (since 1974 first Worthing Sixth-Form College and more recently Worthing College), and then St Peter's College, Oxford, where he gained a Master of Arts in physics.
Stanhope joined the Royal Navy in 1970, was confirmed in the rank of sub-lieutenant on 1 September 1972, and was promoted to full lieutenant on 1 May 1977. Promoted to lieutenant commander on 16 October 1982, he commanded the submarine HMS Orpheus from 1982 to 1984. After receiving promotion to commander on 30 June 1986, he commanded the submarine HMS Splendid from 1987 to 1988. He became a teaching officer on the Submarine Command Course in 1989.
Promoted to captain on 30 June 1991, Stanhope then went on to command the frigate HMS London from 1991 to 1992 before becoming Captain, Submarine Sea Training in 1993. He was appointed Deputy Principal staff Officer to the Chief of the Defence staff at the Ministry of Defence in 1994 and then attended the Royal College of Defence Studies in 1997. He commanded the aircraft carrier HMS Illustrious from 1998 to 2000 during which time that ship was deployed on operational patrol off Sierra Leone. Promoted to rear admiral, he became Director of Operational Management at NATO Regional Command North in 2000 and was seconded to the Cabinet Office in 2002 before being promoted to vice admiral and becoming Deputy Commander-in-Chief Fleet in July 2002.
Promoted to full admiral on 10 July 2004, Stanhope became Deputy Supreme Allied Commander Transformation at NATO that year. In November 2007 he became Commander-in-Chief Fleet and took the honorary position of Vice-Admiral of the United Kingdom.
Stanhope succeeded Admiral Sir Jonathon Band as First Sea Lord and Chief of the Naval staff in July 2009. In June 2011, during operations around Libya, he warned that the fleet would only be able to sustain operations for around 90 days after which the Government would have to rebalance priorities. On 24 June 2011 The Daily Telegraph confirmed that Stanhope, in common with the Chief of the Air staff and the Chief of the General staff, would lose his position on the Defence Board, the highest non-ministerial Ministry of Defence committee, which makes decisions on all aspect of military policy. He was succeeded as First Sea Lord and Chief of the Naval staff by Admiral Sir George Zambellas in April 2013.