Cloud service brokerage has been identified as a key concern for future Cloud technology research and development. Integration, customization and aggregation are core functions of a Cloud service broker. The need to cater to horizontal and vertical integration in service description languages, horizontally between different providers and vertically across the different Cloud layers, has been well recognized. In this chapter, we propose a conceptual framework for a Cloud service broker in two parts: first, a reference architecture for Cloud service brokers; and second, a rich ontology-based template manipulation framework and operator calculus that describes the mediated and integrated Cloud services, facilitates manipulating their descriptions, and allows both horizontal and vertical dimensions to be covered. Structural aspects of that template will be identified, formalized in an ontology and aligned with the Cloud development and deployment process.