Right now there's the Kylo Ren comic that fleshes out the character's downfall and his early relationship with Snoke and the Knights. It's not over yet but presumably will end with him properly joining the First Order, with Luke probably telling Han and Leia the bad news before going to his exile.
With all the Palpatine stuff that happened in ROS I think there's probably going to be some EU that's going to flesh that out much like the comic is building on the bits of Kylo's origin revealed in TFA and TLJ (and to a much lesser extent ROS). "Prince of the Empire" could make for an interesting title IMO.
Of course number one is his survival. Is he, like in Dark Empire, in a clone body? Or were his remains somehow recovered from the DS wreckage, possibly by Ochi (Who obviously knew where the wreckage was with the dagger), and taken to Exegol? Also, why he waited, created Snoke, etc and what role he had in influencing Ben through Snoke, and also unanswered questions about the Sith Eternal, who seemed partially distinct from the FO at first.
But most importantly, his family. Going by the actor's age and Rey's own presumably his son was probably born around the time of SOLO or REBELS, where the Empire was pretty much at the height of it's power and hadn't really faced an organized rebellion yet. Also did Palpatine raise him before he presumably fled to Jakku? Was Vader aware of his existence etc?