* A kingdom or domain: In this sense, opposites could be anarchy, chaos, disorder, or a state of no governance.
* A sphere of activity or interest: Here, opposites could be irrelevant, extraneous, outside the scope, or unrelated.
* A supernatural or magical world: This might be the mundane world, the real world, reality, or the physical world.
To determine the best opposite for "realm," you'd need to consider the specific context in which you're using it.