Banishment was a punishment that put the recipient into a state of exile.
Leela was banished from the Sevateem for blaspheming against Xoanon. (TV: The Face of Evil)
While pretending to work for the Vardans, the Fourth Doctor banished Leela from the Capitol, knowing that her single-mindedness could have exposed his duplicity as the Vardan possessed telepathic abilities. (TV: The Invasion of Time)
Angboda banished Thaur, Vulsturg the Vast and Jotastar the Just from Norsum. (COMIC: The Screaming Prison)
The early Time Lords banished Fenris the Hellbringer to the Zone of No Return for his supposed murder of Omega. (COMIC: 4-D War)
The Eternals banished the Carrionites to the Deep Darkness. (TV: The Shakespeare Code)