Within industrial manufacturing, most processing steps are accompanied by transporting and positioning of workpieces. The active interfaces between handling system and workpiece are industrial grippers, which often are driven by pneumatics. On the way to better energy efficiency and digitalization, companies are looking for new actuation technologies with more sensor integration and higher efficiencies. Commonly used actuators like solenoids and electric engines are in many cases too heavy and large for direct integration into the gripping system. Shape memory alloy (SMA) actuators are suited to overcome those drawbacks of conventional actuation systems, because of their high energy density. Additionally, they feature self-sensing abilities that lead to sensor-less monitoring and control of the actuator element. Another drawback of conventional grippers is their design, which is based on moving parts with linear guides and bearings. These parts are prone to wear, especially in abrasive environments. This can be improved by a compliant gripper design that is based on flexure hinges and thus dispenses with joints, bearings and guides. In the presented work, the development process of a functional prototype for a compliant gripper driven by a bistable SMA actuator for industrial applications is outlined. The focus lies on the development of the compliant kinematics, where first results of FEM simulation are discussed. As a result, a working gripper-prototype which is manufactured with modern 3D-printing technologies is introduced.