unknown error 4000 my iPad will not 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

If you continue to experience difficulties with direct update from iPad Settings, you may have more success if you perform the update using a PC or Mac computer. To do so you will need access to either a PC (with iTunes 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.

There are known issues with update of some iPad models (such as the iPad Pro 10.5) to iPadOS 15.0.1/15.0.2/15.1. 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.