Connect the game to the same Facebook or King account on the new phone that you were using on the old one.
If the game is not connected to Facebook or a King account on the old phone, then connect it first to save it and then connect the game to the same account on the new phone.
If the game is not saved anywhere, try these steps to sync it with a King account:
Open the game on the old phone and tap the Settings on the game's Start menu, then tap the Cogwheel and finally the button called Account.
If you already are on the game map, go back to the Start Menu where the 'Play' button is.
On the Start Menu tap the Cogwheel and finally the button called Account. Choose 'Register with an email' and follow the steps.
When the game is connected on the old phone, open it on the new phone and on the Start Menu tap the Settings > Cogwheel > Account and choose the button in the bottom where it asks 'Already have a King account?'. Log in with he email and password you registered on the old phone and the levels will be synced!