Since Kit asked, let’s throw some ideas into the pot.
The Time Lords
Do we need them? Russell T Davies got rid of them (and then brought them back and promptly got rid of them again) because The Last Of The Time Lords is more interesting than The Most Human-Friendly Of The Time Lords. Likewise, the Doctor doesn’t need to be a Time Lord - the original plan was that he be a human from a dystopian future trying to stop it happening.
We should probably keep these guys. Historicals would be a lot harder without them.
Merchandising would never forgive us. But we can certainly mangle their history. Maybe they aren’t from Skaro, or maybe we’re there at a new version of their Genesis. Maybe the Kaleds and Thals are still kicking around. As long as you keep the EXTERMINATE! attitude, anything goes. Maybe they hover by default, having round bases. Maybe they’re totally round, just folding out weapons and eyestalks as needed. Or they’re ten feet tall! And make more variants! Merchandising would love us!
It’s been done. But it could be done again. They could be former humans from a nightmare future, travelling back to make themselves possible. Mr. Davies had already had the idea for the Toclafane in case they couldn’t secure the rights to the Daleks, so that idea could fit the Cybermen. Or indeed the Daleks! Consider a puppet/CGI version in the style of The Flood. See BOTIS for modular Cybermen design ideas. But anyway, make more variants! Merchandising would love us!
Where to go with him that we haven’t before? Depends on the Doctor, really, as the Master is ever his shadowy reflection. One option noted waaaaaay back is to make him a professional but callous Time Lord agent who clashes with the Doctor over their methods. Or like one iteration of the Leekley series, he’s in charge of Gallifrey and only the Doctor opposes him. Or a great thief or assassin, but who is he working for if not his own amusement? Or he’s like a more vicious Meddling Monk, playing with time because who can stop him?
Let’s make them even shorter! Four foot two, about as wide, keen on charging at opponents and knocking them over like battering rams. Little Juggernauts with something to prove to the entire universe.
No more sneaking around and grabbing people - the invasion of the surface world is achieved with mole machines!