Whooboy, if you thought the fanboy bigots frothed over Jodie Whittaker...

[Norgarth]

Okay.  Google search gives this: https://youtu.be/4F84WapAH7M
Which is Matt Smith passing the torch to Peter Capaldi.  Apparently, I was wrong, as the companion in question IS Clara, the improbable woman.  Still, back tracking from there should give the desired data.  In the meantime I still have a scene where my fanfic self is going after Judge Claude Frollo to finish writing.

*nods* I recall thatin that special he stated that his current life (Matt Smith's) was his 13th/last life(the War Doctor, and an aborted regeneration using up the last 2 slots) Clara managed to talk to Galifrey, there was no verbal response but they did send energy which resulted in him being able to regenerate once more.

... I seem to recall seeing at some point that the twelve-regeneration limit is social/legal, not biological. Am I mistaken?

It was a bit of both, but plot events extended the limit for the Doctor after Eleven's era. Even she's not sure how many lives she has now.

This matches what I recall as well. The Doctor's regenerations may have been reset or the limit may have been removed entirely