We have two cats. Tigger, who will be 15, tolerated our first Yorkie only because I think he had enough sense to be afraid of the cat. And I think Tigger never messed with him because the Yorkie was here when he arrived.
When we got our second Yorkie after the first died, it was bedlam. Tigger hated Ozzie from Day One. We have had to keep them apart -- or suffer the consequences.
About four years ago, Ozzie made the mistake of padding after me into the family room (Tigger is Lord of the Lower Level) and before I could react, Tigger had attacked him and they were in a ball on the floor. I really had to smack Tigger to get him to release. Poor Ozzie's ear was nearly shredded and he had a huge scratch down the bridge of his nose. Over the next few days, I found all kinds of sores along his body where Tigger had just sunk in all of his claws.
Last summer, we took in a stray kitten, Toby. He started attacking Ozzie almost immediately. Poor Ozzie is just such a sweetie. All he wants to do is play. He barks at him occasionally, but he has never made an attempt to harm him. Oz is a little scared of the kitten (who is now bigger than him) but we have slowly tried to socialize them. Ozzie is very jealous when I hold the kitten but overall he has adjusted well. What's funny is that if one of them settles down, the other tries to "rush" the other one. But no violence to date. We hope eventually, they might even play together.
All of that said -- introduce them slowly. Watch them like hawks. If you can hold and pet both at the same time, do that, all the while gently urging them to check one another out. But don't force the issue or someone may end up bloody!