The Cloister Wars were a series of conflicts fought long before the Time War.
According to human historians, these wars were waged sometime after the Sontaran invasion of Gallifrey, which was the first event to reveal the existence of the Matrix to the wider universe, but long before the Last Great Time War. Seeking to claim the vast amount of knowledge within the system, various species attacked the Cloisters that held the Martix under the Capitol. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe) The Time Lords themselves said the wars were fought early in their history and were the period from which the prophecy of the Hybrid emerged. (PROSE: Dalek Combat Training Manual)
The Time Lords defended Cloisters during the wars; Missy later implied an incarnation of herself, the Master, and an incarnation of the Doctor during their early lives were involved in the wars. (TV: The Magician's Apprentice) The Cloister Wraiths, as always, defended the location as well. (TV: Hell Bent) It was said the Dalek Empire was the first to strike against the Time Lords, who by this time were already their ancient enemy.
Seeking to learn the secrets of the Time Lords and obtain prophecies about what the future held for their homeworld, Skaro, a scouting party of bronze Daleks entered the Cloisters and the Matrix, marking the first Dalek effort to steal Gallifrey's secrets. Instead, these Daleks entered an eternal torment when they were lost within literal mists of time, trapped within the maze (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe) and wired into the Cloisters by the system, being forced into becoming defenders of a location they had attacked. (TV: Hell Bent) The same fate awaited the other species who broke into the Cloisters throughout the conflicts; these species included the Weeping Angels, the Cybermen, and the Krillitane. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe)
The wars were mentioned by Missy to Clara Oswald when explaining how long she had cared for the Doctor. (TV: The Magician's Apprentice) A Cybus-type Cyberman was present in the Cloisters when it was visited by the Fifth Doctor, Nyssa, Tegan Jovanka and Vislor Turlough. (COMIC: Ophiuchus) While in the Cloisters, the Twelfth Doctor and Clara encountered a trapped bronze Dalek and hypothesised that it may have been there since the Cloister Wars. (TV: Hell Bent)
The research of Dalek historians recounted the wars, including noting that it was rumoured the Dalek team that had entered the Cloisters were still trapped within the maze, all begging to be exterminated after being wired into the Matrix. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe) Indeed, the Dalek encountered by the Twelfth Doctor and Clara had asked for the same, though the Doctor believed there was nothing they could do to help it. They also encountered a trapped Weeping Angels and a Cyberiad-type Cyberman. A Cybus-type Cyberman stood motionless a short distance away from that unit. (TV: Hell Bent)