You will need to go back to the nomination form submitted by this councillor at the last election, assuming they were elected (even if unopposed). The form requires the candidate to specify the basis on which they qualify to stand as a candidate and there are a number of boxes they may tick. If the councillor ticked only the box relating to residency, they cease to be a member on the day they move away. If they ticked any of the other boxes, either individually or in addition to the residency box, they may continue to serve as a councillor until the next scheduled election, then seek re-election with a new nomination form based on their circumstances at that time.