Data streams are commonly used by data controllers to outsource the processing of real-time data to third-party data processors. Data protection legislation and best practice in data management support the view that data controllers are responsible for providing a guarantee of privacy for user data contained within published data streams. Continuously Anonymising STreaming data via adaptive cLustEring (CASTLE) is an established method for anonymising data streams with a guarantee of k-anonymity. However, k-anonymity has been shown to be a weak privacy guarantee that has vulnerabilities in practical applications. In this paper we propose Continuously Anonymising STreaming data via adaptive cLustEring with GUAR-anteed Differential privacy (CA...