As long as you use the same Apple Account, if you previously purchased Premium Service, you can use it on other devices for free.
On the Other screen, tap Premium Service, then tap Restore, and your purchase will be applied.
If it does not work, make sure the Apple Account set in the App Store app is the same one, restart your device, and try again.
If it still does not work, tap the Purchase button again to run the purchase process once more. If you have purchased before with the same Apple Account, you will not be charged twice; a message will tell you that your previous purchase will be restored, and the purchase will be applied.
In rare cases, it still does not work or the Purchase button cannot be tapped. In that case, please reinstall the app in a way that keeps your data, as follows.
Open the Settings app, tap General, then iPhone Storage, select this app, and tap Offload App.
This removes the app while keeping its data.
After that, search for this app on the App Store, install it again, and check. Thank you.