Jenkins and Kubernetes Design Involving GitHub
I would use the webhooks GitHub provides if you don't need something specific from Jenkins (Jenkins is in many cases a consumer of GitHub events/webhooks).
https://docs.github.com/en/developers/webhooks-and-events/webhook-events-and-payloads#push
Using this webhook you could inspect each payload for specific parameters (ref, repo, etc...) and do something (like pull) if those parameters are met. In either case, you will need a service that can process the webhook/payload and perform the work/automation.