Doctor Who gave fans the shocking reveal that there are many more Doctors than those that have been featured in the TV show. With this information, there's a huge ret-con over the number of regenerations audiences assumed the character had been through.
This change means that there are perhaps hundreds of variations on the character that could be explored in future books, episodes, or perhaps even the comics. They could have very different personalities or gimmicks that set them apart from some of the other versions of the character that audiences have seen in the series.
Villainous
There have been a few iterations of the Doctor that have seemed as if he could be evil. The Dream Lord for instance was one of the villains that he faced up against, that was supposedly a version of himself.
The idea that there's an evil Doctor out there isn't a new concept but certainly is ed by the fact that there are a variety of other Doctors and one of them is bound to be cruel.
Soccer Fan
Soccer, or football in the UK, is one of the most popular sports in the world. It's probably crazy to think that there has yet to have been a football-mad Doctor (apart from Matt Smith's short on-screen career).
The sport is very representative of British culture, so much so that it makes sense to combine these two very national things. It's a fun gimmick that could be used for a one-off character.
Mad Scientist
The Doctor could be considered to be a mad scientist but hasn't quite entered the Doctor Frankenstein phase of his personality yet. It could be that this is the time to do so.
It would be a fun minor character to see the Doctor constantly preoccupied with crazy experiments, with a lab assistant rather than a companion and perhaps a few self-created monsters.
Teenager
It would be hilarious to see a teenage version of the character take on his mortal enemies like the Master. The character has aged up and down numerous times, with the changing nature actually becoming an ongoing joke.
He's never aged down to his teenage years though. This would make him perfect to go undercover in a school, but he'd also be quite out of his depth for many of his adventures.
Adventurer
There's a lot of adventuring archetypes to copy. Whether it's Nathan Drake or Indiana Jones. While the David Tennant version had elements of these, the idea can be pushed further.
Perhaps the sonic screwdriver can be replaced with something more swashbuckling and the newest hat can of course be an indie inspired fedora, fit for any adventurer.
Vigilante
The superhero genre is pretty big at the moment, but Doctor Who has already seen a Christmas episode with a superhero as part of the main plot. The Doctor would make an excellent vigilante.
Perhaps a younger version of the character sees themselves as a galactic hero and wears some kind of costume similar to comic book sci-fi rather than the vibe the show normally follows.
Silent Warrior
The silent warrior is a character type that doesn't often fit the Doctor. He is rarely stoic and usually talks his way out of any situation, no matter how dangerous it is. It's what the character is actually known for.
There's a danger that the essence of the character is lost like this, but there's an argument to be made that by making the character have a vow of silence for regeneration, he could learn a lot.
Gallifrey Councilman
The Doctor has hated Gallifrey for some time, even though it's his home planet. He believes that the way it is run is corrupt, but there's perhaps a much deeper story here.
It wouldn't be too surprising if the character was at one stage part of the council, but was removed due to actually having a moral com. This could be quite an interesting story and a way to bring back Rassilon.
Environmental Warrior
The Doctor has always cared about the environment, but it would be quite the change of pace to see him become a full on activist, spending his time flying across the galaxy and campaigning for Earth.
Their normal hippy aesthetic would be too easy to apply here, so it might be more interesting to take a completely different approach with the appearance of this version of the iconic Time Lord.
Politician
Politics has played into the show in a large way. It's difficult to forget that the Master once had a stint as a Prime Minister, as did Harriet Jones, who has become quite the iconic character throughout the show.
The Doctor would make an incredible Prime Minister and could help to explain how he also became the President of the whole planet. Perhaps the PM Doctor would launch a mini-series that sees how the politics and alien-fighting interact.