Papal Mainframe

The Papal Mainframe was the ecclesiastical leader of the Headless Monks. (REF: Doctor Who: The Encyclopedia) She gave Colonel Manton, a member of a seperate faith, permission to lower the hoods on headless monks — an act that was otherwise a level one heresy.

The Mainframe was referred to with feminine pronouns and had a female voice when talking to one Cleric. (DW: A Good Man Goes to War)

Being called a "mainframe", she was likely an artificial intelligence.