The last time we saw Kong was in 2017's Kong: Skull Island, though considering that movie was set in 1973 and the titular monster was quite a bit smaller than Godzilla, there's been a lot of speculation about what brings the beast into man's world (and how he increases in stature).
Those are questions which will be answered by Godzilla vs. Kong next year, but an upcoming prequel comic book series set before the events of that movie shed some light on plans for the Titan.
Called Godzilla vs. Kong: Kingdom Kong, it won't be released until next year, but offers some very exciting hints about what's to come.
"[The] upcoming Kong prequel graphic novel will follow a group of highly skilled military pilots gathered together on Skull Island to see who has 'the right stuff' to take on a dangerous mission into the Hollow Earth."
"One of the pilots, Audrey, is haunted by the memories of a monstrous clash with one of Godzilla's titanic rivals that left deep scars. When Skull Island is attacked by Camazotz, a bat-like Titan, Audrey must come to terms with her inner demons, and finding his home newly threatened, Kong must rise to face this usurper that would plunge the world into perpetual night."
It's definitely sounding like the rise of the world's Titans is what disturbs Kong's slumber on Skull Island, and seeing as Godzilla is their "King," that could be why Kong decides to target his fellow Kaiju.
We'll have to wait and see when Godzilla vs. Kong is released on May 21st, 2021.