General Hux was first introduced to Star Wars fans in The Force Awakens as a ruthless, high-ranking General in the First Order and one of the few that reported directly to Supreme Leader Snoke.
Hux’s biggest moment in the films thus far was in The Force Awakens when he gave a speech to his legions of Storm Troopers, declaring that day the “last day of the Republic”, before using Starkiller Base to destroy the Republic home world, along with several other neighboring planets.
Throughout The Force Awakens and The Last Jedi, Hux was shown several times to be in conflict with Kylo Ren for Supreme Leader Snoke’s approval, as well in a power struggle for control of the First Order.
After Supreme Leader Snoke’s death, Kylo Ren declared himself the new Supreme Leader and therefore, Hux’s superior. Hux initially refutes Ren’s claim to be the new Supreme Leader, but affirms Ren once he uses the Force to choke him, proclaiming “Long live the Supreme Leader.”
On the planet Crait, during the First Order’s assault on the Resistance’s base, Ren orders his men to fire on Luke Skywalker, but Hux goes against him and says to focus on the escaping Resistance members. Ren then uses he Force to slam him into a wall and knock him unconscious.
Seeing as the two are clearly in conflict with each other, I can very easily see Hux meeting his demise at Kylo Ren’s hand in Episode IX.
Regarding how it happens, I believe it could be as simple as Hux going against Ren’s wishes and being choked to death with the force, similar to the way Darth Vader did it to an officer in The Empire Strikes Back, or so Ren can take full control of the Storm Troopers, which still appeared to be under Hux’s control.
I could also see Kylo Ren going “mad with power” in Episode IX and Hux try to take the opportunity to usurp his as Supreme Leader, only to be killed for his betrayal.
No matter how it happens, I think that it is a safe bet that General Hux’s story comes to an end in Star Wars Episode IX.