What should Chibnall do with the Time Lords?

Nothing.
They’re hiding and the Doctor is pissed off at them *several billions of years worth of torturewill do that*

I don't think the Timelords need to be tackled, that is until someone has a good story for them, I don't want or think that the Timelords should be shoehorned in somehow.

There are some things I do want to know

1) What is the status of the Timelord society/civilization now? I mean, they are recovering from a devastating war, massive political changes and a social system in disarray.
2) Why hasn't the war restated? The Timelords and Daleks are both back, what is preventing them from going over it all again?

I hope Chibnall does something different with them beyond the confines of classic series continuity, dare to be bold about the Time Lords. One good thing with Hell Bent is there seemed to be actual change to Time Lord society post-War. Hell Bent starts with Rassilon essentially a military dictator (makes sense in light of the War leaving Gallifrey far more militarised than it ever was in the classic series), he sends a gunship to a defenceless village! It also show that finally the Time Lords have got over their obsession with Rassilon, with the Doctor's arrival being the catalyst for them to finally abandon him. Another major shift of attitudes has been about the Doctor who's gone from being the pariah of Gallifrey to its saviour and also that Gallifrey has gone from splendid isolation from the universe to actively hiding from it. My main gripe with Hell Bent is it then ditched these interesting lines of thought to talk about Clara, but I digress.


So more along that line of thought, how has Gallifrey changed post-War, would be nice. Realistically I expect if Chibnall wants to bring the Time Lords into a story it'll be more Genesis of the Daleks or Terror of the Autons style, which could work just as well in giving a glimpse into what the Time Lords are like in modern Who. 

Actually that might be the only thing that could be an interesting story arc. The possibility of a 2nd Time War & what The Doctor (& the rest of the universe) would do to prevent that.

 Both species fought a war across all of time and space, but now the Daleks just cannot find them? That never made any sense to me.

Glue them to plates like dead mice.

I believe that the Daleks and Time Lords who made it out are just a shadow of what they were in the War. There's no way the Daleks we've seen since then are powerful enough to wage a war that threatens the very fabric of the universe and the Time Lords are reduced to hiding at the very end of time, hoping nobody finds them. 
But once they've rebuilt... Then the universe will be in trouble. 

As to what Chibnall should do – Time Lords slowly reasserting themselves could be interesting. I'd only want to see him use them if he can do something interesting with them, though. He shouldn't feel obligated to use them just because they're back. 

I think that would make some sense - they're hiding at the end of time but they're still the same pompous self-important know-it-alls they've always been. So while I'm sure they're dying to interfere and manage the cosmos again, they'd need an agent to do that...

Ollistra would be a great character to bring across from Big Finish to do that. I don't think it would be too hard to introduce her in a way that doesn't require you to have listened to Big Finish.