Can I keep my teenaged rooster in the coop and run with new chicks once they're ready to move in? Thanks 

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Thank you, I'll make sure to watch carefully too.So you'll need to treat this as you would chicks-to-teens/adult integration, and the chicks will need to be penned in an area where he can see but not touch them for 1-2 weeks before allowing him to have contact with them.
Once you're ready to try the chicks with your cockerel, pick a day where you'll be available to supervise so you can jump in if needed if things go south.
Thank you soooo much! I've made notes and will put your great advice into action.So you don't have the chicks yet. I assume they will be a day or two old when you get them. And you are in Georgia, that's good information. That 4x8 coop may be kind of small for an integration but you should be able to make it work.
I basically agree with Rosemarythyme. House them where they can see each other, provide separate feeding and water stations, and give them as much room as you can, all the typical integration things. But if you have electricity in the coop I'd suggest you consider putting the brooder in that coop. Some people like to wait a few days but I put my chicks in the brooder in the coop straight from the incubator or post office.
To me the advantages with this are many. They grow up with that rooster which should make integration easier. They already know to return to the coop to sleep when you let them out. By being exposed to him really early they can start working on any flock immunities they need immediately. I like to do that to strengthen their immune system plus I can better observe them while they are still in the brooder. As you are in Georgia you don't have harsh cold weather at night to deal with. Your problem is more likely to be keeping them from overheating. Before long you may only need heat at night, if then.
I have no idea what will happen with that single rooster. It's always possible things could go bad, but many roosters help broody hens take care of their chicks. There are several stories on here where a rooster takes over raising the chicks if something happens to the broody or after she weans them. To me this is another reason to get those chicks out there as soon as you can. If he sees them at a young age he'll probably assume they are his and will be more likely to take care of them or at least not attack them. If you wait until they are mostly grown he's more likely to not welcome them.
No matter how you approach it I cannot give you any guarantees. You definitely need to do any integrating when you can observe. Good luck!