Apple Pencil not responding to iPad screen

No mention here of your iPad model - or that of your Apple Pencil.

Different models of iPad support different Apple Pencils. Here is Apple's definitive compatibility list for Apple Pencil and iPad:

Apple Pencil compatibility - Apple Support

Outside of the stated compatibility, Pencils are not interchangeable.

Assuming that your iPad and Pencil are compatible, ensure that the user-replaceable Pencil tip is snugly screwed into the body of the Apple Pencil; when fitted correctly you should see a tiny gap, of about the thickness of a sheet of paper, between the tip and pencil body. If slightly loosened, or overtightened, the Pencil may not work properly, if at all.

Be aware that if your iPad screen has ever been replaced by anyone other than Apple, the screen will not be properly calibrated; this situation is known to cause issues with the Pencil. Also, if the Pencil has been dropped onto its tip, or if the tip has been subjected to unnecessary force, the transducer element that its located beneath the replaceable plastic tip may have been damaged; a damaged Pencil cannot be repaired - only replaced.

If you need assistance, the technicians at the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP) will be able to fully test and assess your iPad and Apple Pencil:

Genius Bar Reservation and Apple Support Options - Apple

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, especially 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.

Gentle warming of the Pencil (such as placing on a hot water radiator), prior to attempting charging of the Pencil, can sometimes resurrect a dead Pencil battery.

You still haven't provided any details of your iPad model and Apple Pencil. With benefit of more information, contributors here may be better able to help with troubleshooting.