In conditionally automated driving, drivers do not have to monitor the road, whereas in partially automated driving, drivers have to monitor the road permanently. We evaluated a dynamic allocation of monitoring tasks to human and automation by providing a monitoring request (MR) before a possible take-over request (TOR), with the aim to better prepare drivers to take over safely and efficiently. In a simulator-based study, an MR + TOR condition was compared with a TOR-only condition using a within-subject design with 41 participants. In the MR + TOR condition, an MR was triggered 12 s before a zebra crossing, and a TOR was provided 7 s after the MR onset if pedestrians crossing the road were detected. In the TOR-only condition, a TOR was provided 5 s before the vehicle would collide with a pedestrian if the participant did not intervene. Participants were instructed to perform a self-paced visual-motor non-driving task during automated driving. Eye tracking results showed that participants in the MR + TOR condition responded to the MR by looking at the driving environment. They also exhibited better take-over performance, with a shorter response time to the TOR and a longer minimum time to collision as compared to the TOR-only condition. Subjective evaluations also showed advantages of the MR: participants reported lower workload, higher acceptance, and higher trust in the MR + TOR condition as compared to the TOR-only condition. Participants’ reliance on automation was tested in a third drive (MR-only condition), where automation failed to provide a TOR after an MR. The MR-only condition resulted in later responses (and errors of omission) as compared to the MR + TOR condition. It is concluded that MRs have the potential to increase safety and acceptance of automated driving as compared to systems that provide only TORs. Drivers’ trust calibration and reliance on automation need further investigation.