If you purchased a full, paid version of an app, you can install it for free on other devices with the same account or devices using Family Sharing.

Here is a guide for setting up Family Sharing: https://support.apple.com/en-us/HT201088

As of early 2021, App Store also allows sharing in-app purchases (including subscriptions) across different accounts. You can simply download the app on your device and then tap on the Restore button in the app (usually found in Parents' section or Settings) to restore full content.

Please also make sure that your iOS is up to date: https://support.apple.com/en-us/HT204204

Another way to download the app if the above does not work:

Go to the App Store, tap your account button in the upper right corner, tap "Purchased," and then select the account that was used to make the original in-app purchase. Then, try downloading the app again from that screen.