As already suggested by stedman1, begin by ensuring that you don’t have beta profile installed. If a beta profile is present, installation of production software updates may be inhibited. This support page provides the necessary information to remove the beta from your iPad:
How to uninstall iOS beta software - Apple Support
If the iPadOS 16.2 update still doesn’t appear, perform a forced-restart of your iPad:
Force restart iPad (models with Face ID or with Touch ID in the top button)
If your iPad doesn’t have the Home button, do the following:
- Press and quickly release the volume button nearest to the top button.
- Press and quickly release the volume button farthest from the top button.
- Press and hold the top button.
- When the Apple logo appears, release the top button.
After the iPad restarts, look again for the update.
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. 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.
