If you are using an Apple device, you can connect or disconnect your Apple ID in the game settings.

Tap the gear icon on the game's Home screen to access the Settings screen. There you will find a blue "Save Your Progess" button. Touch the blue button and then you will find a black "Sign in With Apple" button. To connect your Apple ID. 

Note: Connecting your Apple ID will only sync your level and brilliance. Since coins and hints are device-specific, it will not sync these items.