Update software on older iPad

There are different ways to ensure the highest iOS/iPadOS that your device will support is installed on your device but iPad Air1 will only update to iOS 12.5.7

This support article has instructions about updating an iPhone or iPad wirelessly --> Update your iPhone or iPad - Apple Support

You can also use Mac and PC computers to update system software, as outlined in this support article --> Update iPadOS - Apple Support

Use this support article to identify your iPad model --> Identify your iPad model - Apple Support and then the list below to find out what your iPad is capable of running. Alternatively --and somewhat easier-- is to simply try updating it and see if it will update. When updating, your device will update to the highest version currently available that it will support, or it will just say it is up to date (and can't go any higher) and won't install anything. Apple indicates ( Unable to update my iPhone 6 Plus from 12… - Apple Community ) I need to point out the obvious and state that if you want to run a higher system version than your current device will run, that you need to buy a newer device.

If you have the original iPad Air, you cannot upgrade the software any further than 12.5.7.

No.

Your 2013 iPad Air is, simply, too old.

Sorry.