Do you have a few more details? As in numbers of both groups and ages. Hideouts help, sometimes breaking up the original birds into two groups, and adding the new birds to one group. Get them settled. Then add back. It can be tricky in small set ups.
It depends on the chickens. Anywhere from a few minutes to months to never. It's affected by the ages of the chickens, by their individual temperaments, and by the conditions they're living in.
Edit to add: I hope that doesn't sound too discouraging. Most of time, people get things settled down within a few weeks or so.
NatJ is right. It's different in every situation and it doesn't stay the same. With my juvenile pullets and hens (5 1/2 months) the pecking order is changing constantly and now a couple of them are getting brave enough to challenge the old ladies. It is important to have hiding places and escapes. Sometimes you have to isolate the one(s) being bullied, although I found it more effective to isolate the biggest bully. Most of the time it settles down to only an occasional peck to remind them of who's boss, but it pays to be vigilant in case you have to rescue the tormented ones.