Bennett was born in Perth, Western Australia, and educated at Perth Modern School and the Royal Military College, Duntroon, from which he graduated as a lieutenant on 14 December 1948. With 13 other new officers, he was posted in March 1949 to 67 Infantry Battalion, The Australian Regiment, then in the British Commonwealth Occupation Force, Japan.
Bennett served in Japan until September 1950 and then embarked with the 3rd Battalion, Royal Australian Regiment for Korea where he served for a year during which he was wounded in action on 14 October 1950, remaining on duty, and Mentioned in Despatches in 1951. He served again for 12 months in Korea from 1 September 1952 as Senior, then Chief Instructor with the 25th Canadian Infantry Brigade Jnr NCO School while posted as Tactics Instructor at the School of Infantry in Seymour, Victoria.
On return to Australia in 1953 he became Adjt 1 PIR in PNG. In 1954 he was Adjt with 16 Inf Bn (CMF) and in 1956 Staff Capt A in HQ W Comd Then in 1957–58 he served in the United Kingdom with the Royal Marine Commandos and saw duty in Malta, and operational service in Cyprus. He then served as OC 2 Cdo Coy from July 1958 to June 1961, and after attending the Australian Staff College, became the Senior, then Chief Instructor at Officer Cadet School, Portsea from 1962 to 1965. He was then posted until 10 July 1967 to Army HQ which had moved to Canberra in the early 1960s from Melbourne.
He then commanded the 1st Battalion and for service in Vietnam in 1968–69 and was awarded the Distinguished Service Order. On return from UK Joint service training in 1971 he became Colonel Coordination in the office of Chief of the General Staff and in April 1974 was promoted to brigadier, Chief of Staff at HQ Field Force Command in Sydney until December 1975.
He attended senior officer training at the Australian Staff College first long course in 1960–61, Joint Services Staff College in UK as a student then exchange instructor 1969–71, and then the Royal College of Defence Studies in UK in 1976.
He commanded the 1st Division 1977–79, became Assistant Chief of Defence Staff 1979–82, Chief of the General Staff 1982–84 and Chief of the Defence Force in 1984 (the position having been changed from Chief of the Defence Staff). He retired from the Army in April 1987.
During his period as governor, he was called on to be the adjudicator of a sensitive constitutional problem following the inconclusive Tasmanian state election in 1989. The Liberal Government of Premier Robin Gray had suffered a two-seat swing, leaving it one seat short of a majority. The opposition Australian Labor Party led by Michael Field then garnered the support of the five Green members of the House of Assembly for a minority government in what was known as the Labor-Green Accord.
Gray refused to resign, initially intending to stay in office until defeated in the House. When he learned of the Labor-Green agreement, he asked Bennett to dissolve the legislature and call new elections. Under normal circumstances, Bennett would have been bound by convention to honour this request. However, Bennett refused to do so. He believed that Gray was no longer in a position to govern, and therefore had lost the right to ask for a dissolution. He'd also been privately assured before the formal accord was signed that the Greens would back a Labor government. Gray was thus forced to resign, and Bennett commissioned Field as premier.
Sir Phillip on several occasions also became Administrator of the Commonwealth during overseas visits by the then Governor-General, Bill Hayden.
After retiring from the governorship, Sir Phillip has also served as inaugural Chairman of the Australian War Memorial Foundation. He has been the Patron of the 2 Commando Association (now the Australian Commando Association Victoria) since 1985, Patron of The St John Ambulance in the ACT since 1996 and a past President of the Order of Australia Association (elected National President of the Order of Australian Association in March 1997). Bennett is also the inaugural National Patron of the Royal Australian Regiment Association.
He was appointed a Companion of the Distinguished Service Order (DSO) in 1969 for service as Commanding Officer of 1 Battalion Royal Australian Regiment in Vietnam. Bennett was made an Officer in the Military Division of the Order of Australia in 1981, a Knight Commander in the Military Division of the Order of the British Empire in 1982 and promoted to Companion of the Order of Australia in 1985.
He was award a Mentioned in Despatches for; 'During the period, 9 November 1950 to June 1951, this officer performed the duty of mortar platoon commander through that period. His support of battalion attacks was of the highest order etc.'
In 1983 he was made a Commander of the Legion of Merit and in 1985 the Republic of Korea Order of National Security Medal. He was made an Honorary LLD (NSW) in Oct 1995 for his contribution to military education and the Australian Defence Force Academy. He was made a Knight of St John in 1988 and awarded the degree of Doctor of Laws, honoris causa, by the University of Tasmania in 1992. He was awarded the Centenary Medal in 2001.