You may be able to claim a reduction, an exemption or a discount on Council Tax, e.g. if a house is empty or if the person living there is disabled.
The Welsh Government have created an eligibility checker to help you find out if you are entitled to pay less council tax.
Under Section 13A of the Local Government Finance Act 1992, inserted by section 76 of the Local Government Act 2003, the Council may reduce the amount of Council Tax you are required to pay. The Council may reduce the amount of Council Tax in an individual case or in a class of cases where national discounts and exemptions do not apply.
Read the 'Locally Defined Discounts (Section 13A) Framework' here