Get old version of game from game centre

I'm on an iPad using version 9.3.1.

I recently replaced my iPad.

After restoring from iTunes to my new iPad I went into my Clash Of Clans game before signing into Game Centre. Since I wasn't signed in, it started a brand new game (all my progress was lost). So, then I signed into Game Centre. Tried the game again, but wasn't given the option to restore my old version (with all the progress). After searching for a way to do it, I signed out then back in again (to game centre). This is when I found out that while I was in COC (the one without any progress), it was saved into Game Centre, wiping out the version with all the progress.

So, my question is: Can I somehow get back my version from Game Centre that had all the progress?

Thanks