It seems that my iPad Air can not update iOS 13. Is there anything I can do?

It is highly possible that your iPad year and model may not be able to upgrade/update beyond any version of iOS 12, currently at iOS 12.5.4.

The 2013 iPad Air 1, iPad Mini 2 and 2014 iPad Mini 3 cannot upgrade beyond any version of iOS 12.

Sorry.

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 are now 7 and 8-years old, in 2021.

Sorry.

Third party app support, typically, continues for 2-3 years AFTER Apple ends full support of a subset of their devices.

The last major update to iOS 12 was in 2019, with iOS 12.3.

So, it has been nearly two years after, already, and third party app support is already on a downward trend for all iOS 12 supported devices.

Look for many more third party apps dropping support for all iOS 12 supported devices as another year progresses.

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.

If you need OR ONLY able to purchase older, less expensive iPad models, look at older IPads from 2014 and later.

All of these older model iPads below CAN run the latest iPadOS versions and the up and coming iPadOS 15.

2014, 9,7 inch screen iPad Air 2 models

2015, 7.9 inch screen iPad Mini 4 models

2015-2017, 12.9 inch screen iPad Pro models. ( 1st gen Pencil support )

2016, 9.7 inch screen iPad Pro models ( 1st gen Pencil support )

2017, 10.5 inch screen iPad Pro models ( 1st gen Pencil support )

2017, 9.7 inch screen iPad 5th gen models

2018, 9.7 inch screen iPad 6th gen models ( 1st gen Pencil support )

2019, 10.2 inch screen iPad 7th gen models ( 1st gen Pencil support )

2020, 10.2 inch screen iPad 8th gen models. ( 1st gen Pencil support )

Get the largest internal data storage model you can afford as NO Apple iOS device has expandable storage.

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

Sorry & Best of Luck to You!

If you decide to go down the path of purchasing used, secondhand Apple devices, here is how to avoid purchasing an Apple iOS/iPadOS device with user activation lock, in the future.

If you purchase any iPad, or any Apple iOS device, for that matter, used/second hand, online, or even in-person, make sure this iPad does NOT have user activation lock and has been properly reset for sale.

A properly reset for sale iPad should initially power up to an animated, multi-language “Welcome” screen.

DO NOT take the iPad seller's word that this iPad is user activation lock free,

We have seen plenty of used iOS device purchasers get scammed.

User Activation Lock can never be bypasss, circumvented or worked around IF there is no correct previous/original user information to be able to do so.

Apple doesn't get involved with ANY user activation locked, used/second-hand sold devices, either.

So, buyer beware.

If purchasing a used device in-person, power the iPad ON

If the iPad DOES NOT display the initial animated, multi-language “Welcome” screen, then pass on purchasing this iPad.

If the iPad powers up to any other screen, then forget purchasing this iPad.

You cannot trust that the seller actually has the correct needed info to properly reset the iPad back to factory settings right then and there before the actual purchase and exchange of money for the iPad, in question.

Pass on the device.

If you are purchasing this used iPad online ask the seller to provide multiple images, either online or be sent to you via email, showing this animated, multi-language “Welcome” screen of the interested in purchasing iPad model.

Even better, ask for a short video be sent to you showing this animated, multi-language “Welcome” screen, in action and in its entirety, posted to the online ad or emailed to you.

If the online iPad seller refuses any of these requests, pass on the iPad. DO NOT buy.

Good Luck to You!

Correct. You’ll be at 12.5.4.

No. The first gen iPad Air is incapable of running iOS 13