The paradigm of graphene transistors is based on the gate modulation of the channel carrier density by means of a local channel gate. This standard architecture is subject to the scaling limit of the channel length and further restrictions due to access and contact resistances impeding the device performance. We propose a novel design, overcoming these issues by implementing additional local gates underneath the contact region which allow a full control of the Klein barrier taking place at the contact edge. In particular, our work demonstrates the GHz operation of transistors driven by independent contact gates. We benchmark the standard channel and novel contact gating and report for the later dynamical transconductance levels at the state of the art. Our finding may find applications in electronics and optoelectronics whenever there is need to control independently the Fermi level and the electrostatic potential of electronic sources or to get rid of cumbersome local channel gates.