There is no formula for renewing a Mut'ah contract, but only to have a new Mut'ah contract after the end or termination of the existing Mut'ah marriage. When the agreed time of the Mut'ah expires or when the husband terminates the Mut'ah contract, then they will be allowed to go for a new Mut'ah contract with a fresh Mahr and time. There is no renewal formula but only going for new contract.
Wassalam.