Delinquent license fees, as determined by the Council, shall be assessed in addition to the annual license fee except in those cases where, by reason of residence outside the corporate limits, age or ownership, the pet animal was not subject to licensing. In those cases in which an animal becomes subject to the terms of this section during any license year, the license fee shall become due and payable within thirty (30) days after the date that such animal becomes subject to the terms of this chapter. After thirty (30) days, the owner shall pay the delinquent license fee provided by Council resolution, in addition to the annual license fee.