For iOS:

Unfortunately, if your profile was not linked to GameCenter, you will not be able to recover your game. If you had your game linked to GameCenter, then simply log into GameCenter on your new device and you will be able to access your saved profile with your base progression intact.

For Android: 

Currently we do not have a feature that allows accounts to be recovered on Android devices if they are lost or reset. Your saved profile is attached to your device. Unfortunately, we are not able to bring your saved profile over to a new device.