Cloud Service Providers supply services to clients in terms of their demands. They need to be constantly under monitoring for their services with respect to consensus agreements between clients and service providers. A Third Party Auditor or TPA as a trusted organization appears to be necessary to monitor executing agreements of cloud services. Using a third party as an extra component creates cost overheads for clients in a cloud environment. Thus, introducing a cost efficient framework for a cloud environment which includes a third party is an eminent achievement to make a TPA feasible and practical in cloud environments. In this paper, we propose a TPA framework for monitoring service level agreements between cloud service providers and cloud clients using several cloud resources. This framework employs different types of service deployments from various cloud service providers excluding the cloud service provider which is being monitored. Then, we demonstrate that the framework can mitigate costs of a third party auditor in a cloud environment. Simulations of trends for costs exhibits cost efficiency of at least forty percent over ten years when a TPA follows our proposed framework in comparison to other frameworks. Finally, we provide an analysis to compare characteristics of our framework with other frameworks and discuss the advantages of our proposed framework. Our results indicate that TPA as a component of the framework not only reduces overall costs of its presentation in a cloud environment but additionally improves management efficiency and security.