You can't keep them from fighting. Chickens have to determine a pecking order so they know how to live in their society. Once the pecking order is established they can live together peacefully, but establishing the pecking order can sometimes be rough.
I don't know if you plan on quarantining the new rooster or not. That's often a good idea. If you do, I suggest picking one of your existing flock to put with him. Sometimes a chicken will become immune to certain things so no matter how long you quarantine him he won't show any symptoms. And sometimes your flock is the one that is immune but will make a newcomer sick. I prefer to risk one chicken instead of my entire flock.
Your flock has already established a pecking order, but at 3 months, they are getting ready to hit puberty. Even if you don't add another chicken to change the established pecking order, the pecking order is going to change as they mature at different rates. Usually if they have enough room, this is not a big deal. You may not even notice any fighting, just a few occasional pecks.
With two roosters they will have to determine which is the dominant flock rooster as they get older. If they have room, this can involve some fighting but usually it is a quick skirmish followed by a lot of running away. If your space is tight, it makes it more dangerous, both from the pecking order stuff and the dominant rooster stuff.
If you can, I suggest you house the new rooster next to the flock where they can see each other but not get at each other for maybe a week. This won't help the pecking order stuff but it does help them from ganging up on a newcomer as much.
Integration will sometimes go so smoothly you wonder what all the worry was about and sometimes it can be rough. I think how much room they have has a lot to do with it. I wish you luck!!!