Clock-Person

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

Biology
The Clock People granted individuals the ability to alter their own past by correcting mistakes. People who accepted had their timelines erased since it unraveled their personal history. This allowed the Clock People to take their physical place. (EDA: 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 Paterson's experiments, which served as their lifeline. The Clock People were wiped out when the Doctor sealed the breach. (EDA: Anachrophobia)

Behind the Scenes
According to fellow series author Jon Blum, Morris has said that the clock-faced men in the story are meant to be Faction Paradox, although this is not made explicit in the text.