How old are they, the old ones and the new? Age and maturity has a big effect on how to go about this. What do your facilities look like? How big in feet or meters is your coop? How big in feet or meters is your run, if you have one? Photo showing the inside of the coop and how the coop and run go together could be really helpful. For me it's a lot easier to give suggestions that actually apply to your situation if I know what you are working with.
All the questions I would ask....and Ditto Dat.
And what kind of weather do you expect to have when you are going through this? That might make a difference.
Yes......
Welcome to BYC! @AClagg
Where in this world are you located?
Climate, and time of year, is almost always a factor.
Please add your general geographical location to your profile.
It's easy to do, and then it's always there!
Here are some tips about....
Integration Basics:
It's all about territory and resources(space/food/water).
Existing birds will almost always attack new ones to defend their resources.
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.
In adjacent runs, spread scratch grains along the dividing mesh, best if mesh is just big enough for birds to stick their head thru, so they get used to eating together.
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 copious blood drawn and/or new bird is not trapped/pinned down and beaten unmercilessly, 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'(but not a dead end trap) and/or up and away from any bully birds. Roosts, pallets or boards leaned up against walls or up on concrete blocks, old chairs tables, branches, logs, stumps out in the run can
really help. Lots of diversion and places to 'hide' instead of bare wide open run.
Good ideas for hiding places:
https://www.backyardchickens.com/threads/a-cluttered-run.1323792/