Nicholas is my uncle's sister's granddaughter's son. What is the closest possible relationship I can have to Nicholas?
He's your grandson.
This is because:
Uncle's sister would either be your mother or your aunt. But since you have asked for the closet relation, it would be your mother.
Your mother's granddaughter would be either your daughter or your niece. But daughter is the closest.
Further, your daughter's son is without a fail your grandson.