For smooth and successful interactions between human drivers and (partly) automated vehicles (AVs), drivers need to be aware of the current status of the AV, know the limitations of the technology, as well as have a correct understanding of possible actions (e.g., handover of the driving task to the automated system). Therefore, new Human Machine Interfaces (HMIs) are needed that support drivers in the respective tasks and foster awareness of the AVs’ status and possibilities. To reach the full potential of such supporting HMIs, drivers’ trust in the HMI is important, as it plays an important role in the extent to which a system is used. This paper addresses the question of how trust in a newly developed system that mediates between the driver and a (partly) AV (Mediator system) developed over time. The Mediator system was developed in the European project MEDIATOR. It is designed to coordinate between human drivers and autonomous vehicles based on respective fitness levels to perform current and upcoming driving tasks, including environmental factors. To examine drivers’ trust, a driving simulator study was designed. Participants experienced Mediator in several short test drives under different conditions. Results show that drivers have initial trust in the system after receiving detailed information about Mediator and its functionalities. After experiencing reliable and expected system behavior during two trips, drivers trust increased constantly. In the last drive, participants experienced unexpected system behavior (a close approach to a traffic jam with a late and abrupt braking maneuver). The experience caused a momentary decrease in trust, although the overall trust rating toward Mediator after all drives was quite high and even higher as the expected trust. Results indicate that trust in technical systems can be quite robust even after experiencing unexpected system behavior. Adequate trust in the system and its abilities is essential to foster optimal system usage.