When you separate birds, even for a week, it causes a lot of problems. One really needs to treat this bird like a stranger because that is how the flock sees her.
Now chickens are pretty territorial and that works both ways. The flock will defend their space, but they are leary of new spaces. You will see that when you first let them out of the coop/run in the spring. They do not go far, are very hesitant.
This is why very often, keeping a bird in the cage doesn’t work, that becomes her territory not the run that she can see but not go out in.
I have had very good luck with locking her in the coop/run and locking the others out into the yard or free range. At night, put the new bird back to where you had her, let the old ones back in. Do that for two days.
Day three, pick a middle bird and add that to the new bird. There will be a dust up, but one on one generally does not last. It is considerably different than 5 against one.
Keep that pair together day and night, for two days, then late in the afternoon let them out with the others, if they all go to the coop to roost you are golden. If not, you can put them in there if you can get down there early the next day and let them out if it is too rough.
Now there is a difference between a hen attacked by a predator and one that has been bullied by her flock, in the last case, you will need to do some flock adjustment or you will be back in the same situation, culling someone, either the bully or the victim. Pin less peepers, or new run/coop - however this needs to be an immediate solution-chickens will not wait for something to be built. Wishing they would all just be nice won’t work. And we have all been there.
Mrs k