The ever-growing resource needs of modern-day applications regarding guaranteed low latency and the massive data transfer rate are constantly pushing the boundaries of technologies and requiring a paradigm shift. To cater for these escalating resource needs, modern IT computing platforms have evolved beyond the more traditional central cloud/DC with bleeding-edge processing powers and high-capacity networking infrastructure to extend their coverage all the way to the network edge, which may also include the far-edge nowadays. This creates a new paradigm called cloud edge computing continuum (CECC), whereby the services span from core cloud to edge and far edge. To efficiently manage and continuously optimize resources through this new model using the CECC approach, we propose an Agile and Cognitive Cloud-edge Continuum (AC3) management framework. This framework will play a critical role in providing scalability, agility, effectiveness, and dynamicity in service delivery over the CECC infrastructure. AC3 will offer a common and secure federated platform that manages data source, CECC resources, and application behaviour in a unified and harmonized manner to ensure the desired SLA and save energy consumption. Moreover, the AC3 platform can adapt to a different context and events happening in the network, such as lack of resources, data deluge, or mobility of data source, by managing (i.e., deploying or migrating) micro-services across CECC infrastructures. AC3 will leverage AI, ML, and semantic and context awareness algorithms to provide an efficient life cycle management system of services, data sources, and CECC resources for ensuring low response time and high data rate while saving energy consumption.