What the Saxon Master described as a "mutual kicking me out" resulted in his leaving Gallifrey following the Last Great Time War. (TV: Death in Heaven)
History
Though the War Master had escaped the Last Great Time War, (TV: Utopia) his next incarnation returned to Gallifrey on the final day of the war after being embroiled in Rassilon's Ultimate Sanction. (TV: The End of Time) This last day ultimately ended when the planet, whilst besieged by the Daleks, was transported to a another dimension by all incarnations of the Doctor. (TV: The Day of the Doctor)
The Master's battle with Rassilon caused the latter to regenerate into a new incarnation, (PROSE: Pandoric's Box) reportedly because the Master "shoved White Point Stars down his throat". Rassilon screamed all the way through the regeneration, so much that Ohila had to make him "a special draft of potion" to help. (PROSE: Lords and Masters)
Despite Rassilon's previous intention to kill the "diseased" Master, (TV: The End of Time) the Time Lords instead cured the Master's "condition" (TV: The Doctor Falls) and locked him up in Gomer's Asylum, which he later escaped from. (PROSE: Lords and Masters)