Not clear how downtrodden he'd be since he still has an entire great house named for him that has a seat on the council and has featured prominently on the show so far. Although it's possible Kol and Kol-Sha just locked him upstairs, looking down on augment Klingons, and ran the show in his name. Now that they're gone, it's time for Kor himself to show up.
In fact, considering this whole "Remain Klingon" business with L'Rell will probably end in disaster once Voq/Tyler and Voq Jr. are proven alive, Kor can lead an augment revolt with Kang and Koloth and have the augments leading the show once L'Rell is taken down. The Klingons, having been lied to by the previous government, may be willing to let the augments have their shot at doing things, explaining why TOS is full of Augments.
After Kor kills L'Rell, Voq Jr. will leave Boreth vowing revenge for his mother's death, leading him to eventually poison Kor's son and become the Albino.
I'd also love to see Chang and Gorkon, although I don't know if CBS can use movie only characters. And I mentioned interest in a shock twist of having young Kirk as a Section 31 member.
Considering that Kor himself was described as "the last son of the house of Kor" in DS9, it's more likely that he was named after the ancient noble house that he came from, not that he started the house himself.
Kor