Yeah, the idea has been around. This would be one of those things a noble can do during peace time, but nothing too exciting to prevent a war. It could be open for all within range, with a chance of being wounded. A skill could be made for it, but I am not sure if it would need to be visible in any numerical way, nor even trainable in the academy. There would need to be some sort of a reward for the winner, though I suspect a realm wide message stating that "Sir Kepler hosted a hunt in Glorious Estate, Keplerville. Sir Random managed to hunt down a large beast, while Sir Badluck was slightly wounded".
Though I suppose it could influence some stat as well, slightly. It would mostly be about some recognition, which would be important for the new nobility. And to have something to talk about when there is a lull.
A successful hunt might give a bonus to region stats too. The valiant nobles caught a big beast that has been pestering the neighborhood, which improves morale. Or they make quite a catch, and throw some leftovers over to the villagers, or there is a celebration where the villagers can join in in some meager way. A slight boost, but nothing fancy. If it's successful. So good hunters would be appreciated.
Perhaps hosting a hunt where nobody turns up would have some sort of a small penalty too. It would happen.
(fodder: yeah, leadership would work too, very nicely actually)