To start a new game, log out of your current account. Make sure it is connected to a Plarium ID (you can use a fake email to do this). Otherwise, the Log out button will not appear in your Profile. For tips on how to create a Plarium ID, check the article How do I save my game progress? Then, open your Profile and tap "Log out".
Create a new account by tapping "Touch to start" on the main screen.