Simply follow the below-mentioned solution to fix iPad stuck in recovery mode after iOS update:
Step 1: First of all make sure that you have latest version of iTunes.
Step 2: Close iTunes, if it is already opened. Connect your iPad to computer and open iTunes.
Step 3: While your device is connected, force restarts your iPad, but do not release the buttons when it shows Apple logo, wait until and unless it shows “connect to iTunes” screen.
For iPad, press and hold “Home + Top (or Side)” buttons together. Keep holding them until you see connect to iTunes screen.
Step 4: After that when you see the option of “Restore” or “Update”, select Update. iTunes will try to re-install iOS without deleting any data. Wait for some time until iTunes download the software.
Note: If download is taking more than 15 minutes and your iPad screen does not show connect to iTunes, then repeat from step 3.
Step 5: After the Update or Restore completes, set-up your iPad.