How do I pair Apple Pencil A1603 with iPad Air air4

You don’t.

You purchased the wrong version Pencil.

You need to purchase and use the more expensive 2nd gen Pencil instead with a new 2020 iPad Pro or iPad Air 4 model.

Both versions of the Pencils charge and pair differently.

Sorry & Best of Luck to You!

This support page may be helpful with pairing and use of the Pencil with your iPad:

Connect Apple Pencil with your iPad - Apple Support

If you continue to experience difficulties, here is one of the better troubleshooting guides:

https://appletoolbox.com/apple-pencil-not-working-heres-our-troubleshooting-guide/