The only remedy you have is to sign up for the school's refund plan. It typically acts like insurance in the event that your child withdraws before end of year. The insurance plan will pay for the unused/remaining portion of your child's time at the school. You contracted to pay for an entire year when you signed the contract with the school at the time she was accepted. You do not want to be out of pocket. Neither does the school. This is why tuition refund insurance is an important part of your planning for a private school education. Tuition refund policies are in place at every private school regardless of whether it is day or boarding, large or small, elementary/nursery school or high school.
St. Mary's policy is the sort of thing you can expect at most schools:
"To minimize the loss to a family due to early departure or change in boarding status, Saint Mary’s School has established a Refund Plan. Under ordinary circumstances, the Refund Plan will, upon early departure, defray part of any losses which occur due to unused tuition and/or fees which have been paid or are payable to Saint Mary’s School."
Each insurance plan has its own specific conditions and limitations. Read the fine print carefully. Understand what you are purchasing.
Private schools have to meet their budgets. They have fixed expenses during the year. They need to be able to count on a fixed income. That's why you are contractually obligated to pay the entire year's tuition and fees regardless of whether or not your child completes her year.