If you change your device, your game will start with a new Guest account. To access your old account, you need to switch accounts:

Menu → Settings → Switch accounts. Then, select either Facebook, Apple ID, or E-mail, depending on how you've protected your old account. 

If you didn't protect your old account, please open Golf Rival on your previous device and go to: Menu → Settings → Protect your account. You can select if you would like to use Facebook, E-mail, or Apple ID to protect your account.