Competing service providers in the cloud environment ensure services are delivered under the promised security requirements. It is crucial for mobile services where user’s movement results in the service’s migration between edge servers or clouds in the Continuum. Maintaining service sovereignty before, during, and after the migration is a real challenge, especially when the service provider has committed to ensuring its quality following the Service Level Agreement. In this paper, we present the main challenges mobile service providers face in a cloud environment to guarantee the required level of security and digital sovereignty as described in the Security Service Level Agreement, with emphasis on challenges resulting from the service migration between the old and new locations. We present the security and sovereignty context intended for migration and the steps of the migration algorithm. We also analyze three specific service migration cases for three vertical industries with different service quality requirements.