Efficient traffic systems control in large cities, and the complex traffic management of signalized intersections is a challenging task, particularly when dealing with high traffic volumes. The city of Zagreb faces this challenge, as all administrative and governmental institutions are in the historic part of the city, and routes for escorted vehicles have a significant impact on the traffic network. This paper addresses the issue of the impact of unconditional priority for escorted vehicles on the energy efficiency of the urban traffic network in the city of Zagreb. The traffic network model is developed using the PTV Vissim microsimulation software. The evaluation was conducted with nodes (delay, queue length, and number of stops) and network evaluation parameters (CO2 emission, NOx emission, PM10 emission, and fuel consumption). The results show that unconditional priority has minimal impact on energy consumption and exhaust emission in the observed scenario. This is a significant result considering all actions that must be undertaken to manage the passage of the escorted vehicles through the traffic network.