iPad Air 1. generation - The Update number - date of Update - and How to check if it is The right Update

The latest update will always be visible from iPad Settings:

Settings > General > Software Update

If an update is available, it will be seen in iPad Settings. You can find more information about iOS12 updates here:

About iOS 12 Updates - Apple Support

The first generation iPad Air can currently only be updated to iOS 12.5.4

Apple ended major update support for the iPad Air1 in September 2019 - although this model continues to receive occasional “point” security updates - the most recent being released just a few weeks go. The iPad Air1 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 and 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 iPadOS14.

Sorry, I appreciate that this may not be what you were hoping to learn.

I hope this information provides clarity as to your available options - and the limitations of your existing iPad.

If you own a 2013 iPad Air 1, iPad Mini 2 or a 2014 iPad Mini 3, these iPad year and models cannot upgrade beyond any version of iOS 12, currently at iOS 12.5.4.

These iPad models have overall internal hardware that is too old, too underpowered and incapable of running all of the new, advanced and internal hardware resource intensive features of iPadOS.

These iPad models will soon be 7 and 8-years old, in 2021.

Sorry.

There is one last thing you can try/attempt, if you need older versions of apps.

If you own another much newer iOS device that can run iOS/iPadOS 13 and later, you can install the most recent version app/s onto that more recent iOS device.

Then go back to your older iPad, open the iOS App Store, go to the Purchases section of the store app, search for the app/s you wish to try and download to that older iPad and see if an older version of the app is allowed to be downloaded/installed to that older iPad.

These newer iOS/iPadOS devices must use your same Apple ID user account and password.

Failing that OR IF NO joy, then there is nothing more to be done.

It's 2021, now.

If you need/want an iPad with an up to date iPadOS with access to current, updated apps, then you really need to seriously consider a purchase of a new iPad model OR a much, MUCH “newer” and less expensive, refurbished or used iPad models, from better known, trusted sources, like other Apple product/device retailers/resellers, some locally or from online, on the Web/Internet, capable of running the latest iPadOS versions.

There are PLENTY of newer, older iPad models that can run the latest, current versions of iPadOS.

I am sorry that you had to learn all of this, but this does not change any of the facts regarding these very old iOS devices.

Sorry & Best of Luck to You!

Check here:

Go to---> Settings---> General---> Software-update.

The last update for an iPad Air (2013) is iOS 12.5.4

You can't go any higher.

The last/latest IOS update for a 2013 iPad Air 1st gen is iOS 12.5.4.