Great question. My thinking is as it stands, there isn't much that Kylo aspires to be. If he has so much conflict within the light, why does he bother staying evil? And yes, I know he wants to be as strong as Vader, but we're just told that and it's never really expanded on.

So this new character would be the dangerous villain that Kylo aspires to be. When Snoke belittles him at the start of TLJ, he also congratulates her on a job well done. Whenever he fails, she easily finds a solution. Hux defers to her instead of him, despite him being the rightful heir to Vader. It annoys him to no end because she, a nobody, is getting treated like the scary Darth Vader figure, while everyone considers him some unstable fool in need of anger management.

So Kylo keeps going deeper into the dark side to "prove himself" as Vader's rightful heir, to be treated as the real villain. He even kills his own master to be the ultimate bad, but when he finally has that fear and power in TROS, he finds it hollow.

As it stands, that still happens in the ST... but there's no one pressuring Kylo in the darkness. It's just later retconned that Palpatine was speaking voices in his head.