To use your unlocked regions, the World Pack or your Premium subscription on a new device you have to log in with the mail address that is registered in the komoot account you purchased them with. After downloading the komoot app from the iOS App or Google Play Store, log in with your account details and you’ll find the unlocked products under Premium (symbol of a tree in the menu or the three dots that lead to "More") when you scroll down to the regions section. 

If you have already logged in on your new device but do not see your purchase or get asked to purchase again you are logged in to the wrong account. Here is an article on how to sort this out: Purchased maps not available