Council Tax is not applicable to full-time students. Your university should have already informed the local council that you are a student but if you receive a letter in regards to paying council tax, please ask your university for an exemption certificate and forward this to the council, they can then update their records.
For the avoidance of doubt , the decision on whether you need to pay council tax and/or the start and end dates of any council tax exemption, will be made by the Local Authority. Your exemption may cover only the dates of your course which may be shorter than your Tenancy Agreement.