 A Franciscan friar, he was appointed the Bishop of the Diocese of Clogher by Pope Clement X on 22 April 1676.His papal brief to the See was dated 13 May 1676 and consecrated on 14 June 1676.Tyrrell was also appointed the vicar apostolic of the Diocese of Kilmore by Pope Innocent XI on either 9 February 1678 or 21 March 1678.