Official Godzilla 2 novelization explains the relationship between Kong and other Titans

The official Godzilla 2: King of the Monsters movie novelization has a passage within it which references Kong and his relationship with other Titans outside of Skull Island. The passage basically explains that for years Kong heard a few calls of other Titans outside of Skull Island but because they did not directly affect Kong or his Island, he simply did not care. However, as of the 2019 attack involving Ghidorah, who awoken many more Titans, the number of calls from other Titans had increased greatly. These calls also disturbed the dormant Skullcrawlers which lived beneath Skull Island - this is what triggered Kong aggression. Following the 2019 attack Titan activity around Skull Island has increased and ultimately will be forcing Kong to leave his home and go hunting.

The post credits of Godzilla: King of the Monsters also explained this activity via fictional news editorials.

So, that being said we should expect to see some more, larger Skullcrawlers to appear in Godzilla vs. Kong. We should also expect Kong not to play that well with others... his Island is being threatened and rival Alpha Titans are treading too close to his territory. Kong is not leaving his sanctuary to make friends.