If the money does not belong to the school but the school holds the funds, then the school owes the money, that makes it a liability.
So for club-A there should be a liability account showing the balance owed, and the bank account would increase by that amount. (debit bank, credit club-A liability)
when you pay out club funds, the club-A liability account would be the expense account (reason) for the payment, lowering the amount of liability.