how to stop a pony from biting and kicking other horses in the field?

This is a tough situation all around.  I'm surprised the yard owner is tolerating it.Can you ask the owners if he can be turned out with the mares instead?  (If they have mares.)

It's highly likely that they will teach him some herd manners.  He's definitely in need of some.

The other thing that might help him is more exercise.  Ride him more often, longer, and harder.

Make sure you're not overfeeding him, giving him too much energy for noodling the other harses.  Ponies rarely need more than just hay, so cut any hard feed he's getting.

Once he's getting adequate exercise and less energy from feed, he'll have less energy for chasing the others around and be more satisfied just being out.

If this doesn't work, you may have to move yards.  Sooner or later, he's going to seriously injure one of his pasture pals, and you're going to be liable for the vet bills.

He's a horse being a horse. Maybe he's top dog or establishing himself in the pecking order. Biting and kicking is what horses do and you don't need to protect them from that. Locking him up or cutting him off from his herd wont stop this problem. Maybe he kicks and bits when you're around because he associates you with food. Humans usually cause the problem because you can't step in the same river twice and every time you're present you change something. Let them be horses. It's probably all peaceful when humans aren't around and you have no idea why that other horse got kicked. The chances are this horse is top dog and the others might be trying to change the pecking order and move up. They don't need protecting or locking up.

You might need to find a stable with smaller paddocks, so he can be isolated with horses he gets along with. If that is not an option, is there a round pen he can go in? You can't really chase your pony around the yard to stop him, and horses are faster than you, and can kick. Is there feed in the paddock? Is this the potential cause? Of course, horses are supposed to eat most of the day. Hay separated into more piles might help, rather than one huge pile.

You can teach him manners while you are handling him, but besides that you don't have a lot of options, and he will likely continue this unless the horses put him in his place, which sounds like it is not happening.

Most barns have more than one field, and will move the horses around until they get a good fit between the various dispositions. Without that option, you are going to have some potentially angry people who own the other horses.

Ask for a different way to separate these horses. If there is an indoor arena, some barns will allow the horse or pony to exercise in there as long as no one is using it. But once someone needs to ride, the horse will need to go back in its stall. 

Is he on too much feed, too much grain? If he is getting more energy from his feed, he may be more "energetic" than he should.

-Different barn

-Different field

-Round pen

-Indoor arena

-Pay for construction of a smaller area for your own pony

I was going to say he's a candidate for the snip but see he's a gelding, along with your other horses.    I can only suggest you have him with one, or two? of the horses he's not picking on.    Don't be tempted to put him on his own as horses need a companion (or two).

Fence off the two victimised horses.