When adopting a new kitten, it's essential to consider not only its health needs, but those of any other pets in the home. Even if the older cats in the home are up to date on their vaccinations and in good health, it's wise to protect them with a few precautions. After all, every cat is different and can respond to vaccines differently, meaning they can't be guaranteed to always have 100% immunity.
The first thing to do with the new arrival is to isolate her, not only for health reasons, but as part of the natural introductory process. Cats, in particular, do not generally accept new members into their family easily. With cats, the gradual approach is called for, with plenty of patience on the part of the owners.
It could be part of the way Nature intended things to be, in order to enhance the prospects for survival in any animal group. Allowing new ones into the group readily could be risky, so it's wise to hold back and get to know them first, as well as to weed out health problems before the entire group would be infected.
We should follow suit and take the same precautions. However, we do have some advantages, such as veterinary care as a way to introduce preventive care into the mix.
So when the new kitten comes along, get her to your vet as soon as possible for an examination, testing for common infections, such as leukemia, FIV, and parasites, and then administering the first set of vaccinations.
The most common malady brought in by a new cat or kitten is upper respiratory infection. Watch for watery or oozing eyes and a runny nose.
Keep the new kitten in its own area for at least two weeks, with its own food, water and litter box. Never let the other cats use common items until you're sure everyone is healthy and ready to share. Gradually introduce everyone with supervised together time and be sure they're getting along before you leave them alone.