My Apple Pencil 1st gen will not connect to my iPad Air 3

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/

Be aware that if your Pencil has been set-aside for an extended period, unused and uncharged, the Pencil battery may now be irretrievably damaged through deep discharge. In common with all Li-ion batteries, they must always have some level of charge.

The tiny internal Li-ion battery is susceptible to permanent/irreversible damage through being left discharged for long periods. Even some “new” pencils can exhibit signs of failure out-of-the-box if they are “old stock”. 

It is essential that if you have an Apple Pencil that you charge it regularly - whether used or not - so as to protect the battery from deep-discharge. Do not allow a pencil to remain in low-charge state for any period of time - as the internal battery will fail, rendering the Pencil useless. Setting aside an unused Pencil, for extended periods, is a recipe for premature death of the Pencil battery.

If the Pencil Battery has failed, the only remedy is to replace the Pencil. If the battery has failed and your pencil is within its one-year warranty, you should look to having it replaced by your retailer or at an Apple Store.

Some reports suggest that gentle warming of the Pencil (such as a hot water radiator) prior to attempting charging of the Pencil can resurrect a Pencil battery.