If he is as good as you say then between $120-150 dollars for up to 40 mins. Also, make sure sessions are recorded so you always know what is being discussed.
Paying a private rebbe for WHAT??
Tutoring one of your kids in alef beis? Advising you on halachic issues for a new business venture? Learning with you on an ongoing basis as you would with a chavrusah?
Obviously, the applicable rate will depend on where you are located and what services you are seeking from this Rav.
Some goal posts:
Teachers I know charge the amount that will fit parents budget so that the kid will learn.
You might also consider paying more than going rate from your tzedoka money.
3-5 times more per hour than reasonable yeshiva
tuition divided by number of hours