Staveley was born in York, the son of William Staveley and Henrietta Henderson. He entered the British Army in 1798 as an ensign. Staveley fought in several conflicts in the Peninsular War (Battle of Talavera, Battle of Fuentes de Onoro, Battle of Vittoria, Battle of the Pyrenees, Battle of Toulouse, Siege of Ciudad Rodrigo and Battle of Badajoz and many other minor actions). He went to Mauritius in 1821 and served in various roles (deputy quartermaster-general and commandant of Port Louis) before becoming Commander and Lieutenant Governor of Hong Kong in 1847.