We've caught a first look at King Orm already and we know that he would have liked to rule Atlantis alongside his brother. However, as Aquaman will reveal, King Orm will be the main antagonist of the movie.
In this way, he will try to convince the superhero to join him, just like he'll try to do with the other Kingdoms. But he will fail and his true colours will be revealed.
During JoBlo's visit on the Aquaman set, multiple details about the film came to light. For example, JoBlo found out that Unite the Seven is a reference to the Kingdoms and not the Justice League. In this way, all the kingdoms will be represented on the big screens.
As far as King Orm is concerned, the details about his quest were revealed quite a while ago. But only now we found out what weapon Orm needs in order to obliterate the surface dwellers. And this weapon is Atlan's Trident.
In the comics, Atlan is Aquaman's ancestor and one of the greatest kings of Atlantis. However, after he was betrayed by his brother, Atlan sunk the kingdom using one of the artefacts he himself created. It is this one artefact King Orm is searching.
To find the Trident, Orm will attack the coastal cities of the surface dwellers (JoBlo also notes that there won't be massive destruction and carnage depicted). Furthermore, he also helps Black Manta build his suit, to track and kill Aquaman.
As far as the big battles of the films are concerned, JoBlo notes that King Orm will fiercely clash with The Fishermen Kingdom, trying to subjugate them. It isn't said if he'll succeed. However, from what we've learned, the King will do everything in order to see his plans succeed.