Orm and Aquaman have clashed plenty of times in the comics, but it’s possible that in the movie, the former may be more of a schemer who’s working from the shadows to overthrow the latter.
Aside from Orm’s genetic connection with Aquaman being retained (they share the same mother), there’s no information yet on what to expect from Patrick Wilson’s Ocean Master.
He’ll presumably try to seize for the Atlantean throne for himself like his comic book counterpart frequently does, the question is how he’ll go about doing this.
It’s more likely, though, that the cinematic Orm will have the brawn to match his brains, and when the movie’s climax rolls around, Orm and Arthur Curry (as Aquaman was known as a human) will be locked in combat with the fate of Atlantis at stake.