If I delete Clash of Clans on one iPad, and download it on another using the same Apple ID, will it save my progress?
Extracted from the Clash of Clans FAQ:


  Can I continue my game on a new device?
  
  Yes you can, but it requires the use of GameCenter. The only way to transfer your account to a new device is to have the original village linked to a Game Center account. Login to that Game Center account on your new device and you will prompted to load your previous village. 


This post which requires a login, has some helpful instructions on setting up your game on a new device.