Mouri
The Mouri were a group of entities kept in a state of stasis in the inner chamber of the Temple of Atropos on the planet Time, each standing on one end of a hexagonal platform. They wore white garments and had vertical inscriptions on their faces. Although the Mouri were the only known entities capable of controlling time, other species could act as temporary replacements. Similarly, despite being all female, gender did not seem to be a requirement for the function as both Inston-Vee Vinder (TV: War of the Sontarans) and Dan Lewis (TV: Once, Upon Time) acted as temporary replacements.
The Mouri were "assigned" at the beginning of everything as a means of keeping control of time. The Priest Triangles, who were assigned to serve and guard the Mouri, believed that this was done because time in its more natural form was "destruction", even "evil".
When the Temple of Atropos was operational, all time would pass through the Mouri, who would keep it under control. Being in their place could destroy lesser beings such as humans in seconds, but the Mouri were "especially equipped" to withstand the power of time.
Swarm and Azure once attempted to harm the Mouri, leading to them being imprisoned by the Division. Additional precautions were taken to protect the Mouri, such as quantum-locking; they would only become visible if a living being stepped onto the platform. Swarm, Azure and their Passenger forms were specifically excluded as known enemies.
In time, the Flux gravely damaged the Temple, harming two of the Mouri, who began to flicker between their normal appearance and charred, faceless ones. Shortly afterwards, having freed themselves at last, Swarm and Azure returned to the Temple alongside a Passenger. Swarm atomised two of the Mouri, and inscribed the requisite symbols on the faces of Vinder and Yasmin Khan, who were to take their place.
Swarm described Yaz and Vinder as "a short-term repair". In the Thirteenth Doctor's presence, Swarm prepared to let the full force of time begin to blast through them, taunting the Doctor with the claim that they would surely die within seconds as they were not Mouri. (TV: War of the Sontarans)
Behind the scenes
The name "Mouri" clearly has roots in the mythological Moirai, from Greek mythology. Often known as the Fates in English, the Moirai are typically said to consist of three feminine figures: Clotho, who spins the thread of life, Lachesis, who measures the thread, and Atropos, who ended the lives of mortals by cutting the thread.
The Temple of Atropos, borrowing from this mythology, is a mechanism for the thread of time, and Time herself is analogous to Atropos, a figure involved with death through the passage of time.
