If you are using IOS (Apple) device, you can try to recover your game progress by restoring an iTunes backup of your old device on your new device. Here's a quick guide on how to do this:
https://support.apple.com/en-gb/HT201269

If you are using Android device, you can try to connect your old game to Google Play Games, then install Google Play Games on the new device and use the same Google Play account to download both Google Play Games and the game.
Here is how you can connect your game to Google Play Games: go to your game > Achievements > tap on the controller icon.

If that doesn't help, feel free to contact our Support Team directly.