Apple Pencil not connecting

The tags appended to your post suggest that you have an iPad Air 3. This appears to be a bug affecting some users of Air3, subsequent to updating to iPadOS 13.5.x, that seemingly interferes with pairing of the Apple Pencil.

Another contributor, ApplesAreUs, reports having found a workaround solution to this issue:

“... can confirm the issue is iOS 13.5. The only way to pair your 1st Gen Apple Pencil to your iPad Air 3 is to quickly connect and then disconnect power to your iPad then plug the Pencil into the Lighting port. This will fix the issue and will pair successfully

It’s like the quick jab of power to the iPad ‘wakes’ some part of the software into action. I can confirm I’ve tried this on 2 different iPad Airs with same result”.

This discussion details the workaround - and links to the original solution posting:

https://discussions.apple.com/thread/251445258?answerId=252805522022#252805522022

I hope the workaround works for you.

How old is the pencil and how long ago was it charged? Apple Pencil has very tiny battery in it. If the battery is depleted for any length of time, the battery can simply die.