Where Can Doctor Who Go After 'The Timeless Children?'
The Division
The Division are an interventionist arm of the famously non-interventionist Time Lords, doing all the wet-work needed to protect Gallifreyan interests in the universe. This organization has appeared in Doctor Who before; notably an ageing version of the Second Doctor was working for them when found by the Sixth during a storyline called The Two Doctors.
It makes sense that, amongst a people who now have twelve extra lives, the person who has a lot more than that would be recruited to such a black-ops style unit and sent on dangerous missions. However, we don't know the details of any of those missions just yet, as The Doctor had her mind wiped at the end of her tenure.
Tecteun seems to have been involved with The Division and she saved at least some of The Doctor's true past, preserving it in the Matrix of Knowledge. Encrypted to appear as if the memories belonged to some random Irishman called Brendan, until one looked closer, these are the clues that may lead The Doctor to her true home, or at least to a new set of clues.
Once she's escaped from jail, that is.