My pencil is not pairing with my iPad Air

No details here as to your iPad model or Pencil.

Without additional information, the first question must be that of compatibility. Does your iPad support Apple Pencil - and is the Pencil actually compatible with your iPad?

Here is the full compatibility list for Apple Pencil and iPad:

Apple Pencil (2nd generation)

You can use Apple Pencil (2nd generation) with these iPad models: 

• iPad Air (4th generation)
• iPad Pro 12.9-inch (3rd generation) and later
• iPad Pro 11-inch (1st generation) and later

Apple Pencil (1st generation)

You can use Apple Pencil (1st generation) with these iPad models:

• iPad (8th generation)
• iPad mini (5th generation)
• iPad (7th generation)
• iPad (6th generation)
• iPad Air (3rd generation)
• iPad Pro 12.9-inch (1st or 2nd generation)
• iPad Pro 10.5-inch
• iPad Pro 9.7-inch

Not sure which iPad you have? Identify your iPad model.

Assuming that you have a suitable iPad and Pencil, this support page may be helpful with pairing and operation of the Pencil:

Connect Apple Pencil with your iPad - Apple Support

In case of continued difficulties, here is one of the better troubleshooting guides:

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

I can see you are having a case of some sort that allows to store the pencil, but it might obstruct the Pencil from charging/connecting properly. Try removing the case and attaching the pencil directly to the iPad

If the links already provided do not help with resolving the issue, noting that the second generation Apple Pencil must be in direct contact with the iPad magnetic dock to both pair and charge, you would be well advised to seek assistance from Apple Support.

You will find the Get Support Link at top-right of this page. Alternatively, the technicians at the Genius Bar of your local Apple Store will be able to test and assess your iPad and Pencil.

Was it working before? Did you buy the Pencil used or have you had it for a while without it being/getting charged?

That battery is so tiny, it could be dead and it is unable to receive a charge and therefore unable to pair or even be recognized if the Pencil didn't get charged for a substantial amount of time.

Do you really have the iPad Air that was released in 2020? The one without a Home Button?