To start a new account you must first delete your existing account.
Please write in to Support through the in-game settings area with the following message:

Delete my account
Once you have sent this message, your account will be deleted within 30 days.
Once your account has been deleted, the next time you open the app you will begin your experience with a new account.
Please note: once your account has been deleted, we will not be able to reactivate it. Any progress you've made in the game (coins, levels, diamonds, journey) will be lost forever.