Educated at St Catharine's College, Cambridge, Reeve joined the Royal Navy in 1967 and specialized in engineering.^[1] He was appointed Commander of HM Naval Base Plymouth in 1998 and, following promotion to rear admiral in 2000,^[2] he became Change Director at Fleet Headquarters in 2000.^[1] He went on to be Chief of Fleet Support as well as Naval Member for Logistics on the Navy Board in December 2000 before retiring in 2004.^[1]

In retirement he became a Non-Executive Director of Oxford Metrics Group.^[1]