Please make sure your iOS device is one of the supported devices: iPhone 5s or newer, or iPod touch (2015) or newer.
If your device is one the supported devices, the issue is likely on App Store. By searching Internet, there are many threads talking about not being able to install purchased apps. Some people mentioned it might be related to Terms and Conditions need to get accepted:
E.g. try to purchase/download other never installed app, then install purchased app again.
Apple has an official answer to this (not that useful)
“Redownload an app”
If still not working, suggest open a ticket with Apple Support.