It is likely an in-app purchase issue. We are required to use Apple's in-app purchase system for all purchases on Apple devices, which means that in-app purchases must be enabled on the device, payment methods must be up to date, terms agreed with, etc. If in-app purchases are turned off or restricted in any way, the Rent and Buy buttons will not show up, as is described.
You may want to log in at https://appleid.apple.com to see if there are any notifications in the payment area.
Next, on your Apple device, you should open the Settings app, then go to Users and Accounts and make sure there is a user listed under the "Users" heading. If not, you should log into your Apple account there.
After that, on your Apple device in the Settings app, you should go to General, then Restrictions, and ensure that either all restrictions are off, or that the In-App Purchases restriction is set to "Allow".