The iPad Air2 is capable of update to iPadOS 15.7.5. The Air2 does not support iPadOS 16.x.
If your iPad is capable of being updated to a more recent version of iOS/iPadOS than is currently installed, these support pages outline both the available methods by which the update can be performed - and troubleshooting should you experience difficulties:
Update your iPhone, iPad or iPod touch – Apple Support
If you can't update or restore your iPhone, iPad or iPod touch – Apple Support
If your iPhone, iPad or iPod touch won’t update - Apple Support
iOS update and restore errors – Apple Support
Be aware that while an iPad may be capable of update, in some circumstances you may need to use a computer to perform the update (such as the currently installed version of iPadOS being too far behind the current release). To do so, you will need access to either a Windows PC (with iTunes for Windows installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of macOS). Ensure that your installed version of iTunes has been updated to the most recent version; the essential device drivers are included.
Download and use iTunes for Windows – Apple Support
Update to the latest version of iTunes – Apple Support
Update software on iPhone, iPad or iPod touch in iTunes on PC - Apple Support
You should note that for your iPad to install an available update, its battery must be charged to at least 50% capacity - and/or be connected to its Power Adapter. Similarly, the iPad can only be updated over a standard WiFi connection - or be updated by a PC or Mac using iTunes or Finder - over a USB connection.
If you are short of available storage space to perform the update (+4GB recommended), using a PC or Mac computer will require less space to be available on the iPad itself - as the update package is downloaded, unpacked and verified by the computer prior to installation on the iPad.