If you switch to a new Android device, your game progress will be loaded automatically when you log in to log in to your Google Play Games account.
You can continue your progress on multiple Android devices, by signing into the same Google Play Games account and this way your progress will be saved between the devices. Please note that you can have only one game progress attached to one Google Play Games account.
NOTE: When switching back and forth between multiple devices, always restart the game to sync progress. When switching devices, it can take several minutes to load the latest progress.