The Master is a lot better at regenerating as he chooses than the Doctor. He could stay John Simm despite having died properly twice now for this reason, although maybe with another new look? Or perhaps that version has run its course, with The End Of Time being a fitting last hurrah.
Here are several other ideas. Many of which have also been suggested as possible Doctors, of course... A follow-up article runs through five popular options including Bill Nighy and goes “nah” to all of them, except Alan Rickman. Because come on, Alan Rickman!
Sadly, no female Master suggestion - Helena Bonham Carter? Miranda Richardson? Hermione Norris? Gina Bellman?
At one point it suggests that the Master (at least sometimes) deliberately chooses to reflect the Doctor, which is where this idea came from. It keeps him vital, unpredictable, like the Doctor and the series itself.
My first thought would be to run with the Master’s expertise in disguise and hypnosis, as well as a new face, and have the Doctor (and us) meet him without realising it...