A royal hunt was a hunt between predator and predator.
In 2267, to get out of his death sentence from a sham trial, Captain James T. Kirk convinced Trelane that there was no sport in a simple hanging. Kirk then spoke of the terror, suspense, and fun of murder which intrigued Trelane enough to let Kirk suggest an alternative. Kirk offered him a personal conflict, not like the pistol duel they had earlier that day, but the real thing. The stakes were a Human life – his own. After Trelane picked up a sword, Kirk said there still wasn't enough sport involved and Trelane agreed.
Challenging Kirk to a royal hunt, Trelane told Kirk to hide anywhere he'd like in the forest and Trelane would seek him. Kirk then told Trelane that he'd have to make it worth his while and up the stakes: while they played their game, the USS Enterprise was to be free and continue on its way. In return, Kirk would give him a contest he'd remember.
As Kirk attempted to order his ship to leave, Trelane appeared and attacked. Trelane told Kirk that he must try harder because it was too easy. After running further into the forest, Kirk caught Trelane by surprise and disarmed him with a kick. Kirk picked up the sword and swung to strike but Trelane disappeared into thin air. He immediately reappeared and confessed that Kirk scored first. Kirk then threw the sword away but Trelane summoned another one, which caused Kirk to flee and pick up a tree branch for a weapon. It proved ineffective so Kirk fled to Trelane's castle where he became trapped and cornered.
Satisfied with the sport, Trelane decided he'd break the deal because he wanted to play with the rest of the crew. Trelane claimed victory, yet Kirk did not concede defeat. Kirk further defied his orders until two non-corporeal beings appeared, who revealed themselves to be Trelane's mother and father. They put a stop to their child and freed the Enterprise. (TOS: "The Squire of Gothos")