While I have never been a private chef per se, I have worked as sole charge chef/manager in the corporate sector, which is pretty similar, as well as in hotels, restaurants and contract catering.
It sounds like you don't yet have a lot of experience so can I suggest that you get some a la carte or catering experience before you embark on your journey as a private chef? Maybe a short stint at a hotel that does both might be suitable... It will expose you to a wider range of function types and bigger numbers, giving you valuable experience in dealing with a wide range of situations. You sound like a very confident chef but working for someone else will also allow you to make a few mistakes at their expense, whereas if you went straight in to the private sector by yourself, there won't be room or backup for errors.
Hope that helps!Kiwisizzler’s Blog