An image of the Cloisters taken from the entrance transmat
The Cloisters are essentially Gallifrey's haunted basement. The Cloisters houses The Matrix, which the minds of dead Time Lords are stored, and they also contain a set of bells named (you guessed it) The Cloister Bells. The bells ring like an emergency alarm when any sort of catastrophe is about to happen, sort of like a interdimensional tornado siren.
A picture of a Cloister Wraith uncovered from the retrieved corpse of an unfortunate visitor. iPhone 6S so the camera quality is shit.
The Cloisters are defended by entities known as Cloister Wraiths, also known as Sliders. The Cloister Wraiths "neutralize" invading entities and essentially recruit them to help defend the Cloisters. No one has ever entered the Cloisters and left alive, thanks to the Wraiths and their posse of alien creatures.