Welcome to Android Central! It really depends on a couple of things:
1. If the game allows you to log into an online account, like your Google Play Games account or Facebook account, that often means your progress gets saved to the cloud, associated with that account. But you need to make sure it does, since some games only use your account for minor things.
2. If the game saves your progress locally in a directory you can access, then you could probably copy those files to the new tablet (making sure they get placed in the exact same directory that the game creates). The game progress files might not be easily identifiable, though.
Backup/restore apps like Helium might be able to backup your progress and then restore to a new device.