It is possible to use the paid version of the application on multiple devices as long as you are signed in to Google Play or App Store on both devices with the same user account.
Please note that it is not possible to use the application purchased on Android with an iOS device or vice versa as purchases are not compatible with each other.
For iOS, simply download the Anchor Pro application on the new device. If you are logged in to App Store with the same Apple ID, you should be able to open the application, go to Settings -> Anchor Premium and select "Restore Previous Purchase".
For Android, open the Google Play store, ensure that you are logged in with the same account with which you initially purchased the application and you should be able to re-download the application on a new device for free.