The Doctor has settled down once again into semi-retirement-this time, for the past half-century he and his companion, Nardole have been teaching at a British university, but in actually, it’s a cover for a mysterious vault he’s guarding nearby. However, through his informative, poetic lectures, he’s attracted the attention of a local woman, Bill, and she, has in turn, attracted his attention, and he begins to tutor her.
Bill, at a local club, also attracts the attention of a woman who appears to have a ‘star’ in her eye-Heather-and vice versa. However, Heather is alarmed by a mysterious oil puddle on the campus.
Also, Bill notices the Doctor apparently in a reflection of a picture of her mother, oddly enough. (He pulled a similar, slightly creepy stunt with Clara way back).
She also stumbles upon the vault.
When Bill meets Heather again later on, Heather seems to be oddly dripping water. It appears the oil has possessed her and is using her as it’s “Pilot”. As the creature tries to attack the Doctor and Bill, he introduces her to the TARDIS, and the two head first to the vault, where they’re followed by the Oil/Heather wherever it seems to be going, even in Australia on the other side of the world, or in an alien planet in the future.
The Doctor figures out their might be a way to stop the organism-have it meet some “old friends” of his. Yep, Daleks, in a middle of a confict with their old enemies the Movellans.
The oil also possesses the Dalek, but the Doctor and Bill recognize the Dalek eye having Heather’s star. She then briefly melds with Heather-realizing it was her that Heather/Oil was chasing all along-urging her to let her go despite their fondness for each other. The Oil Heather then dissipates.
Back in the present, the Doctor is about to mind-wipe Bill, but after she protests, he decides not to go through with it, although he’s reluctant to bring her on his companion, as he has a promise to watch the vault. But eventually he relents, and his travels begin anew with his two companions….
However, trouble is coming. And it has a familiar face he’s not seen in a while.
Or should I say, faces….