On 24 July 1994, Dunn was ordained to the
episcopate as an auxiliary bishop of Auckland. On 24 December 1994 he was appointed Bishop of Auckland to succeed Browne who had been named Bishop of
Hamilton. Dunn was installed as Bishop of Auckland in
St Patrick's Cathedral, Auckland, on 29 March 1995. New Zealand's bishops first endorsed instead efforts to establish different guidelines for translation rather than a new translation, and in 2017 welcomed Pope Francis' establishment of a commission to review the standards followed in rejecting the 1998 translation. Dunn said the idea was to avoid rules that "impose Latin syntax on contemporary English". In September 2017, Dunn authored an essay in
NZ Catholic on the relationship of the Church to LGBT Catholics. He said that communication comes before judgment and instruction: "For Jesus it was most often friendship first, and conversion second. We all listen most intently to those we love and those whose company we enjoy." He recommended the work of Jesuit
James Martin as a guide, advocating its inclusive language and sensitivity. He wrote that an attitude of respect requires the Church to call people by the terms they prefer rather than
homosexual and called the Vatican's use of the phrase
objectively disordered "needlessly cruel". In 2018, Dunn was the secretary of the New Zealand Catholic Bishops Conference and the episcopal deputy for
Holy Cross Seminary and
Good Shepherd College. ==Resignation==