You really need to consider some things. How many birds, how much space you have, how many birds you have now. How old your birds are, and size and breed of birds.
I generally think of adding birds like + & -. If you get it close to 0, that is the easiest integration kind of sort of.
New birds - are stranger they are a negative, your birds home court advantage...so say you are getting 5 birds, and you have 6. -5 +6 = +1, not too bad.
Younger birds are negative, older birds are a positive, they will be dominant, unless all birds are laying.
So say you have 6 pullets not laying and get 5 laying birds, well now you are a -6 +5 = -1 added to the above, and you are at zero.
It is just a way to think about birds. Not iron clad, but if you are adding 1 single chick to an established flock of 8, I am not saying it can't be done, but it is going to be much harder to get it done, so hard on the chick, that a lot of people won't think it is worth it.
See no touch for a couple of days or weeks some people do, some just toss them together, some somewhere in-between.
Another crucial point is what does your run look like, in terms of square feet, and if it is just a wide open rectangle where every bird can see every other bird at all times. That is a tough place to add birds. You need to add clutter, hideouts, platforms, places to get out of sight, get away from more aggressive birds.
So some pictures and numbers would help us get you through this.