Is it possible my dog will never accept our new Westie puppy?

Two females under one roof. Our 4.5 year old dog is aggressive towards the 4 month old puppy that came home 3 days ago. As soon as the unsuspecting pup comes anywhere close she growls and snaps at it. If they are far from one another she seems indifferent but often keeps a close eye on the poor Westie. We pamper her just as we always have so she does not feel jealous. I worry that things will never change.