Reverse it, put the old ones in the cage, and let the young ones the run of the place.
Or, let the old birds out of the set up into your yard, and then let the young birds be in the run/coop set up. Either of these will let your young birds explore and gain confidence in the new enclosure. And this is rather ungrounded theory, but I think it helps if the old birds can see the new birds in the set up, without chasing them. Let the old birds in shortly before dark, so the urge to roost is nearly as strong as the urge to fight.
Take a good look at your set up. Many times I see runs, where as any bird in any part of the run can see any other bird, not matter where they are. It is just a two dimensional open space.
Put some clutter into it, add some roosts, add some mini walls, add some hideouts, platforms, where birds can get under or on top of. This makes it much more interesting to the birds. Set up feed stations, so that a bird eating at one station is out of sight of a bird eating at another.
It will get better, unless you do not have enough space for your number of birds. I will admit, that sometimes there are certain birds that do not fit into your set up, instead of wishing, you are better off removing them from your flock. They cause a lot of problems.
It would be helpful to add numbers of birds in each group, pictures of your set up, and measurements. If my ideas don't help.
Mrs K