Thanks for your question about your new kitten and Spirit. I am a veterinarian and will do my best to help.
Cats need to make their own relationships, on their own schedule. Whenever I get a new kitten or kittens, I set up a bathroom for the kitten, with her own food, water and litter. Then I block and tie the door so it is open a little bit: big enough for the kitten, but too small for adult cats. That way the kitten can be alone, eat, and come and go as she pleases if she is at all fearful of the other cat, or the new house.
I also try to make the adult cat feel secure, being able to eat without the kitten present a couple of times a day, extra attention and treats.
Catnip for both may help them bond.
If there seems to be a lot of stress, you can plug in a Feliway diffuser. It emits a cat pheromone (odorless to us) that has a calming effect.
Let me know what else I can answer and help with.