By: +David Herron; Date: April 9, 2017
The Master first showed up during the Third Doctor's time. He served a role for The Doctor similar to Sherlock Holmes' Moriarity, in other words The Master is his arch nemesis. That Doctor, played by Roger Delgado, was said to be in his 12th incarnation and therefore by the rules of regeneration was in his last regeneration. The Masters' demand to survive at all costs is part of what's driven his life.
A careful reading/watching of The Masters' appearances in televized Doctor Who, the 1995 TV movie, and some Doctor Who Comics, shows a path. During the 4th Doctor's time, The Master was shown as a shriveled corpse until he stole The Keeper of Traken's body. Afterwards he played opposite the 4th, 5th, 6th, and 7th Doctors. The whole time he used stolen bodies. Then in Utopia he was shown as an old man at the end of the Universe who'd hidden from view by completely burying his memory of being a Time Lord. Was that old man a stolen body? Somehow he managed to regenerate into the John Simms Master, so how did that happen?
The John Simms Master ended in The End of Time when he started fighting Rassilon. Presumably he made a deal with Rassilon. But at the time we thought he'd been pushed into the middle of The Time War, and would have been destroyed when The Doctor destroyed Gallifrey.
But we know from The Time of The Doctor that the destruction of Gallifrey never happened. Instead The Doctor managed to preserve Gallifrey in some hidden dimension somewhere, and that later it made its way back into the Universe several billion years in the future. As seen in Hell Bent.
In The Time of The Doctor, Gallifrey used one of those Cracks in the Universe to open onto Trenzilore, forcing The Doctor into a showdown last stand scenario. At the end of that episode, Gallifrey was shown having escaped back into the regular Universe while also gifting The Doctor with more regenerations.
Presumably The Master or Missy was in existence on Gallifrey at that time. And therefore Master/Missy should have been able to escape Gallifrey in some way. We haven't seen Missy with a TARDIS, but instead a time bracelet like what Captain Jack Harkness used.
Was the Missy body a legitimate regeneration? Or is it another stolen body? That depends on what, if any, deal was made with Rassilon.