Valeyard
Let’s kick off with one for real Doctor Who nerds. Back in 1986’s “The Trial of a Time Lord,” the Sixth Doctor came up against a corrupt Time Lord lawman known as the Valeyard – who turned out to be a darker future version of the Doctor himself. His exact nature was left ambiguous, but it was stated that he was sort of a shadow-Doctor from in between his twelfth and thirteenth regenerations.
Fans who have been keeping track of continuity, then, have been waiting for the Valeyard to appear in the modern series. Now that we have the Thirteenth Doctor, the Valeyard could have been born in between the change from Peter Capaldi to Jodie Whittaker, which means this is a perfect time for the villain to reappear.
If this sounds like something that wouldn’t work because it’s just too fan-oriented, then, OK, there may be some truth to that. But you wouldn’t have to make the history of the character important – just leave it to the fans to join the dots. Regardless of the continuity issues, it would just be interesting to explore an evil version of the Doctor.
Sure, a Matt Smith episode, 2010’s “Amy’s Choice,” previously touched on the idea, but it’s too ripe for potential to leave it at just that.
Clara (And Ashildr)
Usually when the companion leaves the show their storyline is wrapped up in some way – they might be carted off to another universe, get their memories wiped or even, very occasionally, die. The exit of Jenna Coleman’s Clara Oswald, however, only did the opposite – it promised lots more adventures for the character that we’d really love to see.
At the end of 2015’s season 9, Clara was resurrected by Time Lord tech and stole a TARDIS with the immortal Ashildr (as played by Game of Thrones‘ Maisie Williams). As two women who practically can’t die, the implication is that the duo went on to travel in time and space for the rest of, well, time. Given that, it would be kind of unlikely that they would never bump into the Doctor again. So, it would be pretty mean for the show to give us this set-up and then do nothing with it.
Although the character’s creator, Steven Moffat, has moved on, there’s nothing stopping Chris Chibnall from revisiting this part of the show’s history. In fact, Jenna Coleman just returned for a cameo in the Christmas special, which tells us she’s still game for more Clara. The ever-busy Williams might be more difficult to coax back, though.