Your iPad Pro 9.7 is capable of update to iPadOS 15.3.1 - this being the most recently released version. As 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
If you have a beta profile installed, ensure this has been removed from your iPad - as, otherwise, 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
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.
There are known issues with update of some iPad models (e.g., iPad Pro 9.7 & 10.5) to iPadOS 15.x. Do you have a WiFi Only, or WiFi+Cellular model of iPad?
For affected WiFi+Cellular models of iPad, many are reporting that removal of the SIM tray from the iPad will allow the verification and installation processes to successfully compete. Other reports suggest that installing a SIM card (whether active or not) also permits the update process to complete.
You may need to restart the update process, but removing the SIM tray from the iPad is simple and costs nothing to try.
Remove or switch the SIM card in your iPhone - Apple Support
If you have a WiFi Only model, the current workaround is to remove the iPad Passcode - and then re-try the installation process. This has also been observed to resolve issues with installing/verifying the update on WiFi+Cellular models.
Be aware that removing the iPad Passcode has implications for any payment methods registered for ApplePay from iPad - and your Keychain (that includes your saved passwords). Assuming that you have other devices (such as an iPhone), your Keychain will remain preserved in iCloud - and can be easily re-synchronised with your iPad via iCloud. Payment cards registered for ApplePay will need to be manually re-added after the update.