Godzilla vs. Kong pretty much closed the book on the Monsterverse. Both alpha Titans came to an accord, going their separate ways in the end, and it's presumably the close of their conflict.
As far as the movies go, there aren't any current plans for more installments. Legendary's contract with TOHO also expired in 2020, so they no longer have rights to Godzilla or its affiliated characters. Unless, however, the studio decides that it's in their best interest to make another movie, in which case, they may renegotiate for more films. Keep in mind a future installment depends on how well Godzilla vs. Kong does at the box office and on HBO's exclusive streaming service.
Assuming it surpasses expectations, there are plenty of directions where a new chapter in the Monsterverse can go. Kong, for instance, has the whole Hollow Earth to explore. He briefly took a tour, encountering a few hostile residents in the process, but he's only scratched the surface of the hidden world. That presents an opportunity to have Kong unearth a fallen Titan. Ghidorah was on ice until they revived it. Who's to say Monarch won't accidentally wake up another monstrosity while they monitor Kong in his new home?
What Else Is The Hollow Earth Hiding?
There's also the possibility that a young ape is hiding out in the Hollow Earth jungles. If it's only a fraction of the size, an adolescent will try to keep his presence a secret during a massive disturbance. But once the dust settles and things calm down, coming out to get acquainted with Kong sounds reasonable.
Outside of Kong's environment, another well from which new Titans can spring exists. We're speaking of Apex Cybernetics. The tech organization got their hands on a Ghidorah head and batches of Skull Crawlers. So, it's probably fair to assume they have other monsters locked away.
The intriguing aspect is that none of the organization's heads are still alive. Because that's the case, anyone who lays claim to Apex can use all the assets already in containment. And as we mentioned, that could lead to several Titans wreaking havoc once again. In that scenario, the situation would likely come down to Godzilla battling the next monster to take center stage.
Another Godzilla Problem
Another branching off point for the story could see Godzilla reproduce asexually, much like the version in 1999's Godzilla did. Or perhaps Apex figured out how to clone the behemoth. Such a plot would presumably come down to two lizard titans fighting for supremacy, and who wouldn't want to see that.
Apart from the potential scenarios pointed out above, perhaps TOHO will take the lead with their own take on Godzilla. The Japanese-based production company no longer has to be concerned with marketing for a Legendary film to overshadow one of their own, meaning this is the opportune time to release a TOHO movie.
In terms of what they're planning, another clash between Godzilla and one of his longtime foes sounds plausible. The featured monsters, however, will have to differ. Legendary just did Ghidorah, Mothra, and Mechagodzilla, so TOHO will probably choose another beast out of their archive. That way, there's a clear distinction between the American-made films and Japan's version. It's anyone's guess which monster can stand toe-to-toe with the king, but there's a vast catalog of excellent candidates, all of who can give the alpha Titan a run for his money.
For now, all we can do is see what develops. TOHO may produce something in the near future, or Legendary Pictures might renegotiate for another movie deal. It's just a matter of waiting for the studios to decide.