Getting the best from a contractor requires feedback on performance, both informal and formal. Informal reviews and feedback can effectively be undertaken as a part of the peer-review process.
Use review and feedback to see whether the council's systems can be improved or if the terms of the contract may need to be reviewed. Remember that steady incremental improvement is usually far more effective than attempting larger infrequent changes.
Ongoing (weekly/monthly) discussions between the contact persons in both organisations can assist with small changes and updates on current practice procedures.