The development of energy-efficient artificial synapses capable of manifoldly tuning synaptic activities can provide a significant breakthrough toward novel neuromorphic computing technology. Here, a new class of artificial synaptic architecture, a three-terminal device consisting of a vertically integrated monolithic tungsten oxide memristor, and a variable-barrier tungsten selenide/graphene Schottky diode, termed as a 'synaptic barrister,' are reported. The device can implement essential synaptic characteristics, such as short-term plasticity, long-term plasticity, and paired-pulse facilitation. Owing to the electrostatically controlled barrier height in the ultrathin van der Waals heterostructure, the device exhibits gate-controlled memristive switching characteristics with tunable programming voltages of 0.2-0.5 V. Notably, by electrostatic tuning with a gate terminal, it can additionally regulate the degree and tuning rate of the synaptic weight independent of the programming impulses from source and drain terminals. Such gate tunability cannot be accomplished by previously reported synaptic devices such as memristors and synaptic transistors only mimicking the two-neuronal-based synapse. These capabilities eventually enable the accelerated consolidation and conversion of synaptic plasticity, functionally analogous to the synapse with an additional neuromodulator in biological neural networks.