Edward Glover was born 4 March 1943, the son of Edward and Mary Glover; he was educated at Goudhurst School for Boys and Birkbeck College, London (taking a BA Hons and MPhil in History). In 1971, he married Audrey Frances Lush, having two sons and two daughters (and one son deceased).

Glover joined the Foreign Office from the Board of Trade, in 1967, and his diplomatic career included: Private Secretary to High Commissioner, Australia, 1971–73; Washington [United States], 1973–77; Secretary to UK Delegation to UN Law of Sea Conference, 1978–80; on secondment to Guinness Peat Group, 1981–83; Section Head, Arms Control and Disarmament Department, Foreign and Commonwealth Office, 1983–85; Senate Liaison Officer, BMG [British Military Government], Berlin [Germany], 1985–89; Deputy Head, Near East and North Africa Department, FCO, 1989–91; Head, Management Review Staff, FCO, 1991–94; Deputy Head of Mission and Consul-General, Brussels [Belgium], 1994–98; High Commissioner to Guyana and Ambassador to Suriname, 1998–2002; Quality and Efficiency Unit, FCO, 2002–03.

Glover's work for the FCO briefly ended in 2003, with a move to the Department for International Development as short term expert on Macedonia [later North Macedonia], Public Administration International, 2003–05 and Associate Consultant, DFID Support, to the Office of Prime Minister, Kosovo, 2006–07 and to the Ministry of Foreign Affairs, Sierra Leone, 2008. He then returned to the FCO as an Adviser on Foreign Affairs to the Coalition Provisional Authority, Iraq, 2004, then to the Minister of Foreign Affairs, Iraq, 2004–05, and on consular and visa matters to the Foreign Minister, Bahamas, 2006. He also served as Chairman of the Iwokrama International Centre for Rainforest Conservation and Development, 2005–12.