Just be sure to log in with the same Golf Pad account you used on the old phone. Your upgrade and playing history will be restored automatically. There is no need to pay again.
To access the log in screen, go to preferences in the upper right of the start screen, then tap "User profile". There you will see "ACCOUNT" and you can log in.
NOTE: There are three different ways to log in: Google+, Facebook and email. Each of them is different account.