It's about territory and resources(space/food/water). Existing birds will almost always attack new ones.

Understanding chicken behaviors is essential to integrating new birds into your flock.

Confine new birds within sight but physically segregated from older/existing birds for several weeks, so they can see and get used to each other but not physically interact. Integrating new birds of equal size works best.

The more space, the better. Birds will peck to establish dominance, the pecked bird needs space to get away. As long as there's no blood drawn and/or new bird is not trapped/pinned down, let them work it out. Every time you interfere or remove new birds, they'll have to start the pecking order thing all over again.

Multiple feed/water stations. Dominance issues are most often carried out over sustenance, more stations lessens the frequency of that issue.

Places for the new birds to hide out of line of sight and/or up and away from any bully birds.

In adjacent runs, spread scratch grains along the dividing mesh, best of mesh is just big enough for birds to stick their head thru, so they get used to eating together.

Another option, if possible, is to put all birds in a new coop and run, this takes the territoriality issues away.

For smaller chicks I used a large wire dog crate right in the coop for the smallers. I removed the crate door and put up a piece of wire fencing over the opening and bent up one corner just enough for the smallers to fit thru but the biggers could not. Feed and water inside the crate for the smallers. Make sure the smallers know how to get in and out of the crate opening before exposing them to the olders. this worked out great for me, by the time the crate was too small for the them to roost in there(about 3 weeks), they had pretty much integrated themselves to the olders. If you have too many smallers to fit in a crate you can partition off part of the coop with a wire wall and make the same openings for smallers escape.

You can integrate chicks as early as three weeks of age as long as they've been introduced to the flock for a few weeks prior. I use the panic room method of integration. This involves setting up a safe pen with chick-size openings so the chicks have a safe refuge where the adult chickens can't go. Food and water is inside this safe pen so the chicks don't need to compete for essentials.