Probably not but you should speak to a local attorney.
Why not? Because generally speaking to prove one of these torts, you have to meet all elements – and that includes the business relationship has to end and the plaintiff needs to suffer provable damages. Have clients left the trainer because they are unable to attend shows at that grounds with the trainer there? Can trainer prove that was the causative reason (they weren’t also unhappy with care or training or whatever)? Can the trainer prove that any losses are the result of the show grounds owner’s act? Seems hard to me.
Tortious interference comes in a few varieties. Contract requires a contract to exist and for it to be broken. So that’s probably out. Business expectation doesn’t require a formal contract but it does require the relationship between the two interfered-with parties to end, and damages. Doesn’t seem to have happened here.
Then there is the question of intent – the defendant would have to know of the relationship and that his act would likely destroy it. Malice is not an element, knowledge is. is it reasonable for the show grounds owner to believe that the other trainer’s clients will leave because the trainer isn’t permitted to come to his show? you could probably show that he knew the relationship existed, but harder to prove he knows his act would destroy it. there would have to be additional facts to come close, I would think.
I don’t think that loss of possible year end awards would count because 1. you don’t contract to win awards, I hope, and it isn’t really a broken business relationship and 2. proving you lost just because of trainer’s lack of access to the showgrounds would be very hard (I mean, your horse could be lame or you could fall off anyway and not get points at that show…points are not guaranteed…and particularly hard to prove you would have won just because the trainer was there). it’s not impossible, maybe, but I think a judge would be pretty skeptical. Especially since the clients can go, just not the trainer.
This is all blackletter/general law-based, there may be variance in your local jurisdiction. Again, you need to consult a local attorney to make sure of what the laws in your local jurisdiction have to say and how it would apply to your case (looking at writings/precise wording of exchanges between the parties which could change things). and perhaps they will see the merits differently.
others have offered you some good ideas about working it out outside of court.
I am not a licensed NC attorney so this is all theoretical, not legal advice.