Conner is the son of William Ernest Conner and Joan Millington Conner. Having also spent a year at the Oxford Department of Education, soon after ordination he moved into chaplaincy at
St Edward's School, Oxford (where he was ordained priest in 1972 by Kenneth Woollcombe, Bishop of Oxford, in the School Chapel) from 1971 to 1980, and later at Winchester. For a while, he was an examining chaplain to the Bishop of Winchester. From 1987 to 1994 he was Vicar of
Great St Mary's the University Church, Cambridge. He served as Bishop of Lynn from 1994 to 1998, in which year he was appointed Dean of Windsor; in this role, Conner also held the post of Register of the
Order of the Garter and was a
domestic chaplain to
Elizabeth II. From 2001 to 2009 he was also Bishop to the Forces. He was consecrated as bishop on 2 February 1994 at
St Paul's Cathedral, by
George Carey,
Archbishop of Canterbury. His installation at Windsor on 7 December 1998 was attended by Elizabeth II and
Prince Philip, Duke of Edinburgh; he later presided over both of their interments in the King George VI Memorial Chapel on 19 September 2022, after the Queen's committal ceremony. For many years Conner has been closely involved with the selection of candidates for ordination and with the inspection of theological colleges, courses and schemes. He has been governor of a number of schools and colleges. He is an honorary fellow of
Girton College, Cambridge. ==Honours==