Clock-Person

The Clock-People, (PROSE: Out of the Box) also spelt clock-people or clock people, (PROSE: Anachrophobia) were a race of clock-faced humanoids initially native to the Time Vortex, the remains of Faction Paradox members who had clung on to existence after the end of the War in Heaven. They had the ability to corrupt and replace the biodata of other beings to insert themselves into their timelines.

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. The Clock-People developed clock-like faces and had clockwork replacing their internal organs. Once the transformation or possession was complete, they could also turn back time in their immediate vicinity by two minutes, allowing them to erase moments such as being shot, but turning back even this much time caused them to expend a great deal of energy. (PROSE: Anachrophobia)

Origins
When Father and Mother of the Shadow Spire petitioned the loa to show them the survivors of Faction Paradox after the fall of the Eleven-Day Empire, they saw Mathara's fleet invading a sheath echo of the Homeworld. (PROSE: The Story So Far...) Following the Eighth Doctor's destruction of that Gallifrey using the Edifice, (PROSE: The Ancestor Cell) Mathara's fleet fell from the Spiral. Those cultists' souls transformed into "ticking gearwork viruses" that turned their human hosts into empty clock faces. (PROSE: The Story So Far...)

Evacuating the Vortex
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 Eighth Doctor was able to defeat the first wave of Clock-People when he released mustard gas in the base, as the gas had spread to a fatal level before the clock-faced people became aware of it to erase its release, but one of the creatures escaped the attack when it was taken to Station One and infected everyone present. Although the creatures were able to infect the Doctor, he used that infection to seal the breach by possessing his past self and setting the system up so that the breach would only collapse after the Doctor and his companions had arrived at Station One, thus ensuring that he didn't actually change history and thus make himself vulnerable to infection.

Once the creatures were defeated, the Doctor realised that he had been manipulated by Sabbath into a situation where he would perceive the creatures as a threat rather than refugees. (PROSE: Anachrophobia) After their expulsion from the normal universe, they were cast off into the Void Between Worlds. (PROSE: Out of the Box)

On Gallifraxion Four
Now led by Carvil the Resurrected, the Clock-People managed to reenter the universe "through the dreams of a little girl". They travelled back in time to the past of the planet Gallifraxion Four and welded themselves into the biodata of the natives all throughout their history, thus preventing Galactic Heritage, who officially protected the planet from outside interference, from noticing their invasion. The Clock-People-dominated Gallifraxion was one of the planets where the "seed pods" of the Greth landed, but the Clock-People easily overpowered the alien fungus, who later acknowledged that their methods for taking over a world were far superior to its own crude strategy.

As a joke, they put the captured Greth on trial for interference, and sentenced it to exile in the Void, in reference to their own past predicament. They successfully banished the Greth into the Void, although it ultimately returned to the universe thanks to the help of another entity it met in the Void, (PROSE: Out of the Box) the Yssgaroth. (PROSE: Preternatural Nights)

Behind the scenes
Author Jonathan Morris intended the clock-faced men to be Faction Paradox after the events of The Ancestor Cell. This was ultimately confirmed in The Story So Far... in The Book of the Peace Dossier. Jayce Black had previously referred to the "Clockfaced People" of Anachrophobia as "the neverwere ghosts of the Faction, left over from being unwritten" in a Tumblr post.