Third cat integration into household

[bunnit]

I recently got a third cat that needs integrating into a home with two other cats.
The new cat has been with my partner and I roughly a month. To help ease the introductions, I have had the new cat with her own room "safe room" to live in while she gets familiar with the scents etc of the home. We have been letting her out periodically to explore and socialize. This frequently results in aggressive behaviours from the new cat towards the resident ones. This I am almost positive stems from territory issues.

My question is: Is there a way to start to contribute to controlling this behaviour so that the other cats are not completely terrified? I want to get the new cat out of the safe room and into the family as soon as possible.

Thank you in advance,
Tess