If you signed into a new device and need to restore your Captions Subscription:
Sign in with the same method you used to sign up with (eg., Google, Apple, Phone)
Tap "Restore Subscription" on the top right of the app
Additional information
Apple ties your app and subscription purchases to your Apple ID / iCloud account, so please ensure you are logged in with the same Apple ID / iCloud account you originally signed up with.
Please visit Apple Support for more information.