Afterwards, he was ordained a subdeacon on 19 December 1812, a deacon on 3 April 1813, and a priest on 19 July 1814;[1] all ordinations by William Gibson, Vicar Apostolic of the Northern District.

[3] One of his students in Chester was Thomas Grant, (later rector of the English College, Rome and future bishop of the Diocese of Southwark).

Grant's mother had died when he was ten, so when his father's military unit was deployed from Chester, the thirteen year old remained with Briggs's household to continue his education before entering St. Cuthbert's himself; financed largely by Briggs from Lancaster District funds.

[6] On the death of Bishop Thomas Penswick on 28 January 1836, Briggs succeeded as Vicar Apostolic of the Northern District.

[7] On the restoration of the Catholic hierarchy in England and Wales by Pope Pius IX on 29 September 1850, he was appointed Bishop of the Diocese of Beverley.