He was ordained as a priest on 10 July 1976 at St Benet's Church, Monkwearmouth, Sunderland.

From 1987 to 1990 he was the Redemptorist order's superior and the pastor of Our Lady of the Annunciation at Bishop Eton, Liverpool.

He was parish priest at St Mary's Roman Catholic Church, Clapham from 1999 to 2008.

[3] He was appointed the bishop of the Diocese of Gibraltar by Pope Benedict XVI on 18 March 2010.

[2] Heskett was appointed bishop of the Diocese of Hallam by Pope Francis on 20 May 2014,[2] and installed during a Mass on 10 July 2014.