Clock-Person

The Clock People were a race who lived in the time vortex.

Biology
The Clock People granted individuals the ability to alter their pasts by correcting mistakes. People who accepted had their timelines erased, since it unravelled their personal history. This allowed the Clock People to take their physical place. (PROSE: Anachrophobia)

History
The Clock People evacuated the time vortex because of the Council of Eight. They were dependent on the breach in the Time Vortex created by Payterson's experiments, which served as their lifeline. They were wiped out when the Eighth Doctor sealed the breach. (PROSE: Anachrophobia)

Behind the scenes
According to Jonathan Blum, Morris has said that the clock-faced men in Anachrophobia are meant to be Faction Paradox, although this is not made explicit in the text.