Carr's first appointment was as a curate at St Mary's Church, Luton from 1967 to 1971. He was then a tutor and a chaplain at Ridley Hall, Cambridge. While at the University of Sheffield he was an honorary curate at Ranmoor from 1972 to 1974. From 1974 to 1978, Carr was the chaplain of Chelmsford Cathedral. Until 1982 he was also deputy director of the Cathedral Centre for Research and Training. From 1978 to 1987 he was a canon residentiary of the cathedral. From 1976 to 1984 he was also Diocesan Director of Training. In 1987 Carr left Chelmsford to become Dean of Bristol. In 1997 he moved to Westminster Abbey, where later that year he officiated at the funeral service of Diana, Princess of Wales. In 2002 he also officiated at the funeral of Queen Elizabeth The Queen Mother. In 1998 he was at the centre of a controversy over his abrupt dismissal of the abbey's Director of Music, Martin Neary, over accounting practices for professional concerts and recordings occurring outside the abbey. The matter was contested and referred to Lord Jauncey of Tullichettle for determination at the behest of Queen Elizabeth II. While Lord Jauncey's report upheld Neary's dismissal in finding him to be partially at fault, he was careful to note Neary's years of exceptional service and that his actions were not legally wrongful and did not amount to meaningful harm. The finding further criticised the dean and chapter for the manner in which Neary was dismissed, stating that the abbey, "must score gamma minus on the scale of natural justice" and concluding with the observation that, "had the parties been prepared to discuss openly and frankly the Abbey's concerns, to acknowledge that serious mistakes had been made and to consider the reasons therefor, it might perhaps have been possible to avoid the present unhappy situation with all its attendant publicity and to have reached a rather less dramatic resolution of their differences." Carr was made an honorary DLitt of the University of the West of England in Bristol in 1997. On his retirement as Dean of Westminster in 2006 he was appointed a Knight Commander of the Royal Victorian Order on 17 February. As a priest he has the same precedence as a knight of the relevant order. Carr is the author of a number of books about aspects of the Christian faith.
