Can anyone tell me the process for getting permission to fly in a “restricted “ zone near a small private airport?

Hello there. Thank you for reaching out and for sharing these information with us. For us to be able to assist you further with regards to this matter. Kindly please send an email to our DJI Flysafe department at flysafe@dji.com . In addition to this I will post a DJI link where in you can check if a certain location if free to fly your DJI drone of if this location is a No Fly Zone NFZ. Thank you and fly safe always.

https://www.dji.com/flysafe/geo-map