It depends on the new fish. If it's a peaceful fish then the aggressive fish may not stop. I added my foxface after my purple tang had been in the tank for years and the purple went after him non stop. Now they swim together like brothers sometimes pushing each other bickering and then they go on their merry way. I had the leopard wrasse and the purple harassed him until he wouldn't come out from under the sand and then died. I also have a purple fire fish and zebra dart fish that only come out of the rock work to eat and then go back in because of the purple tang.
Most of the time the new fish has to go through initiation. but once he has they should get along for the most part. however if they decide to stay enemies it can continue until wounds or death of one or both occur.
hit and miss, i always add the fish with the lights out and I shorten my light cycle for a couple days,to try to calm the aggression, I even had to use a mirror to try and cure my purple from being the savage she is.