We Now Have 3 Cats. The Newest One Showed Up

We now have 3 cats. The newest one showed up on our doorstep a month ago hungry, dirty, crying and looked quite poorly. We took her to the vet and checked for chip and was none. We had the vet checked for diseases and she was clean. We washed her up and let her come into the house. She is about 3 years old and very affectionate. Our nine year old cat won't have anything to do with her. Our 2 years old cat welcomes the stranger with open arms and licks her and is very accepting. The newest cat will case the 2 year old cat who is smaller and they seem to enjoy that, but more and more the newest cat will come up to the smaller cat and bite her on the back of the neck until the small cat cries and runs away. What is this all about and what can we do about it. We have scolded her a few times but she still does it.