Domnhall Gleeson's General Hux might be completely loyal to the First Order inThe Force Awakens. Thus, Hux will still be around to lead the First Order and bark orders in The Last Jedi.
Hux will play a relatively significant role in The Last Jedi, even if turns out to be relatively small in the grand scale of things. Episode VIII will pick up on many of the plot threads from Force Awakens; as far as Hux is concerned, that means exploring his relationship with Kylo Ren (Adam Driver). Although the two characters are on the same side polticially, there's a deep personal rivalry between them, as The Last Jedi will further examine.
Related: Some Things Will Never Be Revealed About Kylo Ren
Speaking with Screen Rant, Domnhall Gleeson explained Hux's relationship with Kylo and how the General views the Dark Side :
They've always seemed to be adversarial, you know? I think Hux wants to be at the top and he wants to get the crown from Snoke and he knows that Kylo Ren's probably in a better position to get that. So I think this fear and hatred, I think he's a bit freaked out by all the magic stuff. I think that's where he's out with him you, know now?
The insight that Kylo and Hux will be at odds probably isn't particularly surprising to anyone that has watched Force Awakens with a close eye. Although Hux and Kylo Ren are never openly antagonistic towards each other, there is a deep and underlying sense of tensions and hatred between them during the movie, even for those close to the Dark Side. However, it is Gleeson's view of Hux's relationship with Snoke and the Force that are incredibly interesting ideas to ponder in the build-up to The Last Jedi.
Mainly, it illuminates some of the previously unknown power struggles and politics within the First Order. While it was always obvious that Snoke was in command, Force Awakens never really made clear whether Hux or Kylo Ren was second-in-command. Evidently that ambiguity will continue to play out throughout The Last Jedi. That is a potentially fascinating way to go, particularly because Star Wars has rarely explored the idea of a power struggle within the villains where only one of them can tap into the Force.
The dynamic between the Sith, especially between apprentice and master, has been well explored but not between those who aren't Force Sensitive and those aligned with the Dark Side. It's a conflict that has played out in the comics and other extended universe novels and TV series, both currently in canon and in Star Wars: Legends, but it has yet to really make the jump to the big screen Skywalker Saga. It sounds as though that will change with Star Wars: The Last Jedi.