The extensive use of onboard sensors in smart cars enables the collection, processing, and dissemination of large amounts of mobile data containing information about the vehicle, its driver, and even bystanders. Despite the undoubted benefits of such smart cars, this leads to significant privacy concerns. Due to their inherent mobility, the situation of smart cars changes frequently, and with it, the appropriate measures to counteract the exposure of private data. However, data management in such vehicles lacks sufficient support for this privacy dynamism. We therefore introduce PaDS, a framework for Privacy adaptive Data Stream. The focus of this paper is to enable adaptive data processing within the vehicle data stream. With PaDS, Privacy-Enhancing Technologies can be deployed dynamically in the data pipeline of a smart car according to the current situation without user intervention. With a comparison of state-of-the-art approaches, we demonstrate that our solution is very efficient as it does not require a complete restart of the data pipeline. Moreover, compared to a static approach, PaDS causes only minimal overhead despite its dynamic adaptation of the data pipeline to react to changing privacy requirements. This renders PaDS an effective privacy solution for smart cars.