Hi there, I'm Dr. Sara. I'm a licensed veterinarian who works exclusively with cats and dogs. I'm sorry that you've got such a scaredy cat on your hands - I'll do my best to help.
Was your 4 year old cat already in the home when you brought Star home? If so, it's best to acclimate Star to your home by keeping her in her own bedroom to give her time to get used to your home and gradually be introduced to your other cat.
It's best to keep the new cat separate from the resident cat for at least a week, just in case the new cat is carrying anything infectious like an upper respiratory infection. During this time, your new cat's scent will be around and your resident cat can get used to her. By keeping Star in one room, the resident cat can familiarize themselves with her scent but not have to be face to face with her. After her quarantine is up in a week, you can start the formal introduction process by bringing her out of her room, whilst allowing your resident cat to go into her her room (without actually meeting her). This gives her a chance to explore her new home without being followed or frightened by your resident cats, and it allows the resident cats to get a good sniff of her environment.
It's a flexible process from there, depending on how they all interact with each other. If they seem to get along well, then introduction periods are shorter. Engaging them all in play at one time can be helpful - something like getting them all interested in a laser pointer or a special toy. This is a great ice breaker. If there's any tension, then I'd keep them separate while you're not around until you're confident everyone seems to be OK. They will need some freedom to set up their own hierarchy and social group, so unless there's signs of aggression, I try to just treat them all equal and allow them to work out their social status on their own.
Cats who weren't handled much as kittens (like kittens that grow up outdoors or kittens of feral cats) are typically very skittish and may never really acclimate to human contact. It all depends on how much socialization she had as a young kitten and how adaptable she is. I have seen cats who didn't get much socialization that can still come out of their shell, but it definitely takes a long time and a lot of patience.
Cats have a short window of time that we call their "socialization window" in early kittenhood. During this time, everything they see and experience is greeted with innocence and acceptance. If it happens to them during that time, they consider it normal and not scary. The trick is that once that socialization window closes, it's very difficult to get a cat to accept new things and changes in their lives. In cases where cats weren't handled much by people or if they had negative experiences with people during their primary socialization window, they can be always quite shy and skittish.
Calming pheromone products like Feliway can be quite helpful in the process of moving a cat to a new home and helping them acclimate. Another product I'd consider using is the Sentry Good Behavior collar: http://www.sentrypetcare.com/good-behavior/ which contains similar pheromones and is constantly right there wherever your kitty goes. To some extent, unfortunately, this may just be her personality and there may not be a whole lot that we can do about it other than give her the space that she needs to feel comfortable and secure. Sometimes over the years they do open up and begin to trust us as long as we don't damage that relationship, but other times they are just what they are. I myself have owned a scaredy cat - she was a beautiful siamese cat brought to our family clinic for euthanasia because the owner reported that they "had too many cats". I adopted her and found that she never did warm up to any of us. She always skittered out of the room when we'd arrive, and she very rarely ever came to us for attention. The closest we'd get was when it was dinner time, she'd stand around the food bowl as we filled it. She lived a lovely 11 years with me and I let her be herself - I rarely touched her. I figured that was 11 years more than she would have had if I hadn't brought her home.
Now in some of these kitties, they can "open up" a bit when treated with an anti-anxiety medication. My medication of choice for kitties is usually fluoxetine. It can be difficult to do, though, if he is very skittish. I was never able to medicate my own cat consistently because she was difficult to catch to administer the medication - she was so traumatized by the whole affair that it did more harm than good to try to medicate her.
Please let me know if I can answer any other questions for you!!
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