Thanks for trusting me to help you and Moe today. I am a licensed veterinarian with over 30 years of experience and would be happy work with you.
I am not sure if you were planning on confining him or not when he arrives, but when bringing in a new cat, it is best to give him his "own room" for a short while. There are mutiple reasons for this, including making sure he is not incubating any of the contagious cat viruses, like feline leukemia and/or feline aids. If he was not exposed to other cats for awhile previous to coming into your house, he may have already been screened for those however and that would be less of a concern. From a behavior standpoint, it can be a little less threatening to the other cat in the house if his living space is somewhat restricted to start versus being allowed to have full run of the house right from the start. Cats do not really have a hierarchy in the household, like dogs do, but they are somewhat territorial and may be upset if all of a sudden someone takes over their favorite spot or favorite litterbox.
Even when confining him, your other will know he is there and they will be able to get used to his sounds and smells through the door, before he is allowed to mingle full force. Even when you start letting them mingle, I would do it slowly and only when you are there to observe at first. If they are left all out on their own, there may be altercations that occur that you are not even aware of. Depending on what the set up of your house is like and where she likes to hang out, maybe you could alternately confine her in specific areas of the house and let him roam around some also. Eventually, the goal is to allow both to be out at all times, but it is often best to build up to that gradually.
Most cats do not like to live with one another right off the bat so we have to strive to provide an environment where all cats are able to find a place where they feel "safe". That begins by creating an environment of "plenty." There should be plenty of litter boxes, food bowls, climbing towers, toys and resting areas in multiple locations. All the litter boxes and food bowls cannot be clumped all in one place because that forces the cats together, something they may not want to do. If that is not possible due to the layout of your home, another option is to create a time sharing plan. One cat is out in the house for a bit, then put into a room and other is then allowed out.
One other thing I would suggest is a product called Feliway®. Feliway is a synthetic pheromone that mimics the natural chemicals that a cat secretes. It creates a comforting, reassuring feeling that has a calming effect. It is calming to cats in stressful situations such as transport, hospitalization, veterinarian visits, boarding, new environments, pets or people. Feliway® is a product that can be sprayed or used as a room diffuser. It can be purchased through veterinarians and pet stores. In your case, a few room diffusers may help low the tension. LINK HERE
I am also including a link to a website about environmental enrichment for the cats. The Ohio State University has composed this to help cat owners structure the environment to provide adequate physical and mental stimulation. There are numerous medical conditions in cats that are precipitated by stress and multicat households are often those with more stress, even if not perceived by the humans in the house. Hopefully there are some ideas there that you can incorporate to help keep the stress levels under control
OSU Indoor Pet Initiative
If he has had a previously inadequate relationship with humans, it may take some time for him to build up a trust with you as well. Don't push him and give him time to adjust and learn that you are there to provide care and love as well as interaction with him. Over time he will let you know what sort of interactions he likes and you can build on that.
I hope this is helpful. Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please reply so I can clarify for you.
My posted replies are for general education only and not meant as a diagnosis. Only after a thorough veterinary examination can a diagnosis for your pet be made and specific treatments be advised or medications be prescribed.
Good luck with this new addition and I hope everyone is back to normal soon. It sounds promising so far. Please let me know if you have any further questions or if there is any thing else I can answer for you.