iPad isn't working after iOS 15 update

Two basic troubleshootings steps to perform:

A "forced" restart of your iPad:

• On an iPad with a Home button: Press and hold the top (power) button and the Home button at the same time. When the Apple logo appears, release both buttons.
• On other iPad models: Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the top (power) button. Only when the Apple logo appears (it might take 15-30 seconds), release that button (ignore all other screens that might appear).

If the issue persists, something could have gone wrong during the latest update procedure.

I would try to install a fresh copy of iOS/iPadOS. To do this, create a full backup of your iPhone/iPad (1), then restore it to factory settings (you need a computer to perform this step) and, in the end, set it up as new (2).

When done, restore data from your previously made backup (3).

Follow the instructions provided in these support articles:

(1) How to back up your iPhone, iPad, and iPod touch – Apple Support

(2) Restore your iPhone, iPad, or iPod to factory settings – Apple Support

(3) Restore your iPhone, iPad, or iPod touch from a backup

If the issue still persists, contact Apple Support directly using this link:--> Get Support

Regards

Giulio