My older italian greyhound doesn't get along with new puppy?

So I've had my italian greyhound Thunder for 9 years. She's a female, and we also have another italian greyhound thats around 7 years old, and a male. We bought a new italian greyhound puppy today and she gets along really well with the male (Lightning) but everytime she tries to make friends or get close to Thunder, Thunder growls and snaps at her making her cowar away. Is this a normal behavior between same-sex italian greyhounds? or do I need behavioral training with Thunder? any tips? should i react a certain way when Thunder snaps at her or should I let it play its coarse? I want to do the right thing here for both my old dog as well as my new one. PLEASE HELP!!