I take it the modal situation is Starmer wins in 2024 and serves (let's say) two terms as PM which takes us up to c.2033. Predicting that far out is going to be extremely difficult! I can't see any of the current crop of Tories being relevant at that point - on the contrary they are going to be deliberatlely looking for the kind of people nobody in 2022 had heard of (if Starmer loses his second election then maybe the next Tory PM might be someone we know.) Otherwise the only thing I can think of worth betting on would be someone we know in Labour taking over in a Brown/Blair kind of situation. Alternatively, if Sunak wins the next election (very unlikely imo), then it gets even harder to predict!

If Keir wins the next election, and then the election after, does this resolve as Keir, or are we talking the 2nd unique person to be PM after Rishi?

Has to be unique. Starmer then Starmer doesn't count.

You do mean after Sunak's successor right? So the PM after the next PM who themselves is after Sunak?

@ArtaxerxesTripp Yes, the PM after the PM after Sunak. In the US they conveniently refer to people as (for instance) 'the 49th President' but we don't seem to have a widely recognisable equivalent.