I brought home a little 7 week old puppy and my 15 month old yorkie had the same problem
. It does get better though. they now play together . I supervise them, because of course my yorkie is so much bigger then my puppy ! I am scared that my pup is going to get hurt! She is a tough little one, and often times is the one who starts it! Suzi my Yorkie tries to get away from her by jumping on the top of the couch as far away as she can from Miley Boo! Sometimes though, they chase each other all over the place, and paw at each other, it's very cute.
It takes time for the both of them to warm of to each other. especially for the one wo was already there. Make certain you give attention to that one first, before picking up the puppy . I know it is hard to do, but it is important. Give special time to the older dog first. Otherwise your older one could actully end up getting depressed. Give lots lof petting in places where your Yorkie likes to be petted the most and where it helps her/him relax . Talk to her and tell her how you love her ! She needs to know she still is as special as she was before the new puppy arrived.
It took a little over 2 weeks before my puppy a yorkie got to know each other well enough where they would expect each other. The puppy was always ready to play. It was Suzi who was not that happy about it, now she plays with the pup, but I have to watch her, just scared it is too rough.