If the App Developer has updated the App and now requires a higher version of iOS than the iPad is capable - and the earlier version has been withdrawn from the App Store - your only available option is to replace the iPad with a much newer model.
The first generation iPad Air, iPad mini2 and mini3 can only be updated to iOS 12.5.6.
Apple ended major update support for these models of iPad in September 2019 - although they continue to receive occasional “point” security updates, the most recent being released August 2022. These devices cannot be updated to iPadOS 13 (or any later major versions of iPadOS) as the internal hardware does not meet the minimum technical requirements (CPU capabilities and available RAM) for newer versions of iOS/iPadOS.
Some App developers have dropped support for iOS versions preceding iOS 13.x for technical reasons (often because APIs or software libraries upon which they rely have been updated in the new version of iPadOS, making their App incompatible with earlier versions).
Whilst many App titles remain compatible with your iPad, if you want or need to access to Apps requiring the most recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model that supports iPadOS15/16.
Whether or not you are able to update any iPad to a newer version of iOS/iPadOS will be dictated by the iPad model - and the currently installed version of iOS. You can find this information here:
Settings > General > About
Not sure which iPad you have? Identify your iPad model.
Here is a list of the highest version of iOS supported by the older models of iPad (for simplicity - “generations” are shortened to a number) that are restricted in their ability to be updated:
32-bit devices (obsolete)
iPad1 - iOS 5.1.1
iPad2, iPad3 and iPad mini1 - iOS 9.3.5 (WiFi Only models), iOS 9.3.6 (WiFi & Cellular)
iPad4 - iOS 10.3.3 (WiFi Only), iOS 10.3.4 (WiFi & Cellular)
64-bit devices
iPad Air1, iPad mini2 and iPad mini3 - iOS 12.5.6
iPad Air2, iPad mini4 - iPadOS 15.7.1
Newer models are all able to be updated to the current version, iPadOS 16.1.1
- iPad Pro (all models)
- iPad Air (3rd generation and later)
- iPad (5th generation and later)
- iPad mini (5th generation and later)