The Catholic Archbishop of Armagh is Sean Brady, Archbishop of Armagh. The Church of Ireland Archbishop of Armagh is Robin Eames, Archbishop of Armagh.
Prior to the disestablishment of the Church of Ireland in 1871, the Church of Ireland Archbishop of Armagh was entitled to sit in the House of Lords as a Lord Spiritual, along with the other Archbishops in rotation.
Though the island of Ireland was partitioned by the Republic of Ireland and Northern Ireland, all major Irish religions are organised on an all_island basis. Within the Republic of Ireland, the senior bishop in both the Catholic and Church of Ireland faiths is the Archbishop of Dublin who is known as the Primate of Ireland.
See also
Archbishops of Armagh _ Primate of All Ireland (Catholic)
Archbishops of Armagh _ Primate of All Ireland (Church of Ireland)