FAR 4.804-4 details when a contract is considered physically complete.  Specifically, FAR 4.804-4(a)(1)(iii) notes that it is completed when all option provisions, if any, have expired. Based upon your question, it would appear the contract has ended (not necessarily closed out).  Therefore, for any additional requirements a new contract would be required.  

You mention that work still needed to be done but didn't specifiy if that was included as part of this contract.  If the contractor failed to perform within the terms and conditions you may have the ability to seek reperformance on those areas not completed.  However, there are many factors to consider and those are not provided in your question.