Kind of a weird question, but is it possible for a person to undergo grading when they have only received private training, i.e. they do not belong to a sanctioned dojo? Perhaps at honbu dojo?
(I'm not asking for myself, btw. Passed my first grading yesterday for 5th kyuu. Yay!)
We need more information. What country does this person practice in? What style do they practice? What style do they want to grade in? Who was the private tutor? That sort of thing. It all depends on the policies of the individual organization and the personal connections of the people involved.