The Dark Times
According to the Ravager Swarm, the Temple of Atropos on the planet Time was set up by the Division to end the Dark Times. This was achieved by having Time surrender to Space through the Mouri, thus anchoring the Web of Time. Swarm and his sister, Azure, saw this as heresy, (TV: Once, Upon Time) as they worshipped the Eternal Time, who was in fact the embodiment of time itself that had been imprisoned within the Temple of Atropos. (TV: The Vanquishers)
Siege of Atropos
The Fugitive Doctor was sent on a mission by the Division to enter the Temple as part of the Siege of Atropos, which had been taken over by the Ravagers, and reinstate the Mouri. Her, Karvanista, and two other Divison agents achieved this by hiding the Mouri inside a Passenger form, tricking Swarm and Azure into releasing them back to where they belonged. (TV: Once, Upon Time) While Swarm was imprisoned in a containment chamber, where he would remain for all eternity, Azure was hidden within human form as Anna, where she would remain until her release prior to the arrival of the Flux on 31 October 2021. (TV: The Halloween Apocalypse)
The Thirteenth Doctor, whilst inside her time stream, witnessed the Siege of Atropos, with herself, Dan, Yaz, and Vinder taking the places of the Fugitive Doctor and her companions due to the time storm affecting their time streams. (TV: Once, Upon Time)
The inner sanctum of the temple was damaged by the Flux, leaving two Mouri broken. Inston-Vee Vinder and Yasmin Khan found themselves in the temple, and the Priest Triangles demanded to know if they could repair. Swarm (now renewed) and Azure returned to the temple and killed two more Mouri, subsituting Yaz and Vinder in their places. They lured the Thirteenth Doctor, along with Dan Lewis, to the temple, where they revealed what they had done. As Swarm prepared to expose Yaz and Vinder to the full force of time, (TV: War of the Sontarans) the Doctor chose to put herself and Dan in the other broken Mouri's places, where she could control the ensuing time storm and help the surviving Mouri hide four Mouri within the Passenger form that Swarm and Azure had brought to the temple. The Mouri did so, repairing the temple and freeing the Doctor and her companions, however Swarm revealed that time had been broken long enough to release particles of the Time Force. He and Azure departed, with the Doctor and her friends also leaving the temple. (TV: Once, Upon Time)
Swarm and Azure sought to give the Doctor as a sacrifice to their "saviour", Time, an Eternal and the embodiment of time worshipped by the Ravagers. Time, who had been imprisoned in the Temple of Atropos since the Mouri were instated, manifested from active particles of the Time Force to scorn the Ravagers for their failure in freeing Time from Atropos, and to inform them that the final Flux event they had launched from the Division's base had been thwarted. Time punished the Ravagers, destroying them in the process, although Azure viewed it as a form of ascension. When left face to face with the Doctor, Time warned the Doctor that her time was ending, and that no regeneration or life could last forever. It reunited the Doctor, who had been fragmented into three splinters across spacetime, and returned her to her TARDIS. (TV: The Vanquishers)
Behind the scenes
The Temple of Atropos is named for Atropos, a figure from Greek mythology. She is one of the Moirai, or Fates, who are involved with the thread of life. As one of the Three Fates, Atropos ends the life of mortals by cutting the threads, while Clotho spins the thread, and Lachesis measures it.
Borrowing from this mythology, the Temple of Atropos is a mechanism for the thread of time, and Time herself is analogous to Atropos in the original mythology: a figure involved with death through the passage of time. The Temple is controlled by the Mouri, who are evidently named for the Moirai, as well.