The following predictions are based on elements from both Breath of the Wild and Tears of the Kingdom. Reading anything past this point comes with the risk of spoilers. In fact, the entire post is a spoiler, so turn back now if you haven't finished both games. If you have, and you're curious, then this is for you.

The final form of the final boss of Breath of the Wild is a Boar.

The final form of the final boss of Tears of the Kingdom is a Dragon.

The Zonai are an ancient race that used to use the symbol of a Boar to represent Power, the symbol of a Dragon to represent Courage, and the symbol of an Owl to represent Wisdom.

Therefore, I believe that there will be a third game that uses an Owl as the final form of the final boss fight.

I also think that there are some hints as to where the game could be going from here. Breath of the Wild featured a huge overworld. Tears of the Kingdom introduced the Sky Islands and a copy of the huge overworld in the form of a huge underworld called the Depths. So where could a third game possibly go?

I think it will be the Spiritual Realm, the one where 3 major characters went to at the end of the game. I think it's likely that defeating Ganondorf while he was in an "immortal" form gave him some kind of power in the Spirit World, and the third and final game will feature the Spirit World as a major section to explore.

Breath of the Wild's dark elemental power was called Malice. Ganon was a Boar, which represents Power. Malice can be thought of as corrupting Power; Power is not bad in and of itself, but it is very bad when it is wielded with malicious intent.

The same goes for Tears of the Kingdom, which had a dark elemental power called Gloom. In the game, Gloom would break down the spirit and body of anyone it touched. Those affected by Gloom would not recover until staying in the light for a period of time. Gloom works as a counter to Courage. It is probably also useful to think of it as Dismay, or a Lack of Hope.

For the final game in the trilogy, which will be focused on Wisdom, the dark elemental will probably be something confounding or chaotic. The opposite of Wisdom is Folly, and so anything from Chaos to Confusion will cause Folly. I think the purple mists of the Lost Woods in Tears of the Kingdom are a suitable candidate for what the next dark elemental power will behave like. It is something that destroys or works against Wisdom.

The final boss of that game will probably involve an Owl; either you will have to fight alongside a giant owl to save it from Ganon's spirit, or Ganondorf will possess it or something.

Another option in addition to or instead of the Spirit World would be that Link travels far into the future. He will travel so far into the future that Hyrule kingdom has long since flourished and decayed, once again, and the inhabitants of the ruins of the future Hyrule come back to ask for Link's help. I tend to think that's less likely, though. 

That's all I have to say on this game for now. If any of these things happen, it will be something like 7 or 8 years from now. Any sooner than that, and I'll be surprised.