Appointed Air Aide-de-Camp to The Queen on 29 March 1999, he was promoted to air chief marshal, and became Commander-in-Chief RAF Strike Command, and Commander Allied Air Forces Northwestern Europe on 30 March 1999. In 2000 he became Chief of the Air Staff, and was advanced to Knight Grand Cross of the Order of the Bath in the 2001 New Year Honours. As Chief of the Air Staff he advised the British Government on the British air contribution to Operation Veritas in Afghanistan in 2001, and then to Operation Telic in Iraq. He retired on 5 December 2003. In retirement Squire joined the Royal Air Force Volunteer Reserve. He was Chairman of the Board of Trustees of the Imperial War Museum from 2003 to 2011, and Vice-Chairman of the Board of the Commonwealth War Graves Commission from 2005 to 2008. He was also a Governor at King's School, Bruton, and the Deputy Lieutenant of Devon. In 2004 he privately issued a narrative of the combat operations by No.1 (F) Squadron in the Falklands in 1982, entitled 'The Harrier Goes to War'. In 2005 he recorded an extended interview detailing his military career with the Imperial War Museum's Sound Archive. He died of heart failure at the age of 72 on 19 February 2018 at his home, "Lower Park", at Gidleigh in Devon. A funeral service was held at Holy Trinity Church, Gidleigh in early March 2018. A memorial service was held for him at St Clement Danes Church in London on 1 June 2018, the Queen being represented by Lord Craig of Radley. In 1970 he married Carolyn Joynson, the marriage producing three sons. His main personal interest was golf.