Thankfully this is pretty rare but if it happens the CFI is the only one who can resolve it impartially, and take on the student themself if necessary.
The trick is to match the student to the most suitable instructor in the first place.
White anting is the quickest way to beome the most unpopular instructor in the school.
Having one instructor bearing a grudge against another is very damaging, can make people take sides etc and can escalate very quickly. The students pick it up very quickly, and will probably leave.