In this paper, synchronization of two identical discrete-time chaotic systems is considered in networked control environment where communication plays a significant role along with the synchronization performance. A new event-triggered (ET) active model predictive control (MPC) technique is proposed in the presence of constraints. With the help of active control, a linear MPC is sufficient to control a chaotic system. The active controller is not present all the time, rather only activated when a triggering condition is fulfilled. The MPC also solves the optimization problem only when an event is triggered. A triggering condition is designed to ensure a required performance bound. This technique reduces the computational burden as well as the frequency of communication between sensors and controller and controller and actuator. The effectiveness of the proposed scheme is illustrated by two simulation examples. A trade-off analysis between network traffic and synchronization performance, and its dependence on the prediction horizon is done for the considered system. It reveals that an optimum trade-off can be achieved according to the desired requirement.