This work demonstrates dielectric elastomer actuators controlled by the world's first thin-film transistors on flexible substrate operating at 1kV, thereby enabling locally switching high-voltages on DEAs using a low control voltage. The high voltages required to drive DEAs limit their integration in complex systems, such as high resolution haptic displays and multiple-degree-of-freedom robotics. We report here a top-gate, thin-film transistor (TFT) with coplanar electrodes specifically designed to drive DEAs. The TFTs are fabricated on flexible polyimide, using solution-processed zinc-tin oxide, offset gate and thick dielectric bilayer of Alumina and Parylene. The TFT switches reliably at up to 1kV, outperforming on this metric all published high-voltage TFTs. The on-off current ratio ranges from 20 to 200, the saturation mobility is 0.1cm2/Vs, and the threshold voltage is 10V. Our DEAs are designed for maximal actuation strain at 1kV, to match the maximal voltage of the TFTs. The DEA is a diaphragm actuator: a suspended non-prestretched membrane with electrodes on both sides. The circular electrode has a 5 mm diameter and the silicone membrane is 17um thick. A backpressure of 50mbar is applied to the membrane. The TFT is wired in parallel with the DEA. A change of out-of-plane displacement of 350um is achieved with 30V applied to the gate, for a circuit bias voltage of 1.4kV. The TFT + DEA operate reliably for several weeks.