I’m sorry I am quite late to the game in private airports with approaches. There are very few privately owned general aviation fields left in this country. Less than 35 actually. To land at one of these you most likely do need permission, and for instrument use you do need to get a plate of high we have to authorize. These are FAA rules but also protect us from having people come on to private property for our protection. Someone a while back had asked about my airport 20GA and said the man who he contacted was helpful but ‘almost apologetic’ and wasn’t sure he knew what he was talking about. He was correct in saying you need a plate. We are very accommodating to pilots who wish to use the 4500’ airport, but permission is required, just call.