My sister transferred her Clash of Clans to her new iPhone. Now I have the old iPhone. I want to download and play Clash of Clans. Will her Clash of Clans be deleted from her new phone if I delete her Clash of Clans on the old phone?
You can delete Clash of Clans from the old phone and it won't affect Clash of Clans on the new phone.
You should create your own Game Center ID to play on the old phone. This will ensure your games don't interfere with her games. See http://support.apple.com/kb/ht4314 for steps to create a Game Center account if you don't know how to do this.