The first generation iPad Air, iPad mini2 and mini3 can only be updated to iOS 12.5.7. You iPad Air1 is as up-to-date as is possible.
Apple ended major update support for these models of iPad in September 2019 - although they have since received occasional “point” security updates, the most recent being released two years ago in January 2023. 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.
Whilst many App titles remain compatible with your iPad, if you want or need to access to Apps requiring a more recent version of iPadOS than your iPad is capable, your only option is to consider replacement of your iPad with a much newer or current model.
For information, 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 12.5.7
iPad Air2, iPad mini4 - iPadOS 15.8.3
iPad5, iPad Pro (9.7"/12.9" 1st generation)* - iPadOS 16.7.10
iPad6, iPad Pro (10.5"/12.9" 2nd generation) - iPadOS 17.7.3
(*) obsolete
Newer models are all able to be updated to the current version - iPadOS 18.2.1
- iPad Pro 13" (M4)
- iPad Pro 12.9" (3rd generation and later)
- iPad Pro 11" (1st generation and later + M4)
- iPad Air (3rd generation and later + M2)
- iPad (7th generation and later)
- iPad mini (5th generation and later + A17 Pro)