Cooling off period is not a law. There is nothing to state what is the duration. COP is to avoid the entitlement payment of termination benefit. All contract should end at the specific time to avoid payment of termination benefit. Once a contract expires, so if there a another contract inititated by an application for employment, automatically its a new contract. It would be best if you can, by naming it different position and basing on the new application made by the person whom the contract expired.

to my knowledge, it means shall not join the same or subsidiary company for contract on stated cooling period after resignation