All the major recurring Time Lords have been rogues.
The Doctor. The Master. Romana. The Rani. The Meddling Monk.
Borusa, the boss of the whole gang, appeared a couple times and his second appearance was mad.
Have we ever had an adventure where the main opposition came from a Time Lord who was actually doing his job properly?
Romana started that way and was lead astray by a bad influence (or more accurately a Chaotic Good influence) but considering the Doctor's renegade status, a by-the-book Time Lord out to stop paradoxes and keep the timeline running smoothly would work as an ongoing antagonist. It's just a question of finding a suitable fancy title to use instead of a name...
So for your edification, let me introduce The Seneschal.
Keeper of the keys in the great Citadel of the Time Lords, agent of the Lords President, assassin of threats to time. A man of grave demeanour and fastidious dullness who goes unnoticed across countless years and worlds until it's far too late. Because too late is his business.
A not-funny-looking British actor in a dark outfit that's slightly outmoded but not weird for the era he's working in. Not quite Men In Black but not far off, and he acts the part as well, distant and understated but given to turning up mysteriously and asking a lot of pointed questions.
His TARDIS works reliably and the chameleon circuit makes it unobtrusive wherever he goes. His sonic weapon of choice is a plain metal tube with an adjustable pale white light on the end, like something a dentist would use.
The Seneschal goes by various aliases, undercover as someone you'd never really notice unless you could sense a Time Lord in your midst. He is always polite, careful to harm as few bystanders as possible while minimising the damage - although perfectly willing to destroy timelines that should not exist, and sacrifice himself if it will take a regeneration to stop those he fights. Villains hate him because he never rises to their baiting.
His fatal weakness is that he doesn't really care about anything except the preservation of time. If he shows up, reality is in trouble, and not just from what he's there to stop.
Hmm... sounds a bit like David McCallum in Sapphire And Steel... I imagine an adventure where he shows up would be about as much fun for the innocent bystanders, too...