On 2 May 2006, his nomination as Bishop of Ramsbury was announced,[7] and he was consecrated on 22 June 2006.[8][9] He was the last area bishop under that diocese's 1981–2009 area scheme.[10] Following the retirement of David Stancliffe as Bishop of Salisbury in July 2010, Conway was made responsible for the administration of that diocese. On 31 August 2010, it was announced that he would be the next Bishop of Ely.[4] He was elected by the College of Canons at Ely on 18 October 2010, and the election was confirmed by the provincial court on 6 December 2010, at which point he legally became the Bishop of Ely.[11] His installation and enthronement was held in Ely Cathedral on 5 March 2011.[11]
It was announced that Conway was to serve as both Bishop of Ely and Acting Bishop of Lincoln (each half-time) from 1 January 2022.[14] He stepped down as acting bishop on 20 April 2023, and returned to being the full-time Bishop of Ely.[15]
On 24 May 2023, it was announced that Conway was to be translated to Lincoln as substantive bishop diocesan in "autumn" 2023;[16] his translation was effected by the confirmation of his election on 20 July 2023 at St Mary-le-Bow.[17] He was enthroned Bishop of Lincoln on Armistice Day.[18][19]
Views
Following the conclusion of the Living in Love and Faith process in January 2023, Conway stated that he supports "faithful same-sex couples to have their union affirmed in church and for them to receive God's blessing".[20]
In November 2023, he was one of 44 Church of England bishops who signed an open letter supporting the use of the Prayers of Love and Faith (i.e. blessings for same-sex couples) and called for "Guidance being issued without delay that includes the removal of all restrictions on clergy entering same-sex civil marriages, and on bishops ordaining and licensing such clergy".[21]