Not always. It depends how much you receive. They make a decision after it's been settled and will either send you a bill or inform you there is nothing to pay.
Legal aid is often in effect a loan. If you gain any benefit (such as rights to a house, or a financial improvement) as a result of the Court case which is legally aided then you have to pay back the legal aid money out of the proceeds. Sometimes this is done by putting a charge on the house so the payment is made when it is eventually sold.
Legal aid is VERY unlikely to be awarded in a divorce or other family law case now anyway. Most divorce cases are not eligible for legal aid at all. So the question hardly arises.
As eddie says legal aid is not usually necessary in divorce, certainly not in an undefended divorce, it is simply not needed, in a defended divorce it can be given if the correct conditions apply, but today it is unusual to have a defended divorce.
If legal aid were to be given and your financial circumstances improved you may very well be expected to make a repayment depending on the circumstances.