Usually, yes: Council Tax Reduction is administered by your local council and does not normally transfer automatically when you move. Tell your previous council that you have moved and contact the council for your new address to make a fresh application as soon as possible. Eligibility and the amount available depend on the new council’s scheme, your income, savings, household and circumstances, and the award may start from a date set by that council. Check the relevant council’s website or GOV.UK for the application process and evidence required.