Gyrotrons are high-power microwave sources, readily applied in diverse fields ranging from fusion research and thermal treatment of materials to advanced spectroscopic techniques. Here, we provide the cavity design of a 198 GHz gyrotron to generate microwaves with kW level power and a frequency bandwidth of several hundreds of MHz. The design focuses on the interaction cavity, while all other components of the vacuum tube remain unchanged from a currently operational 198 GHz, 60 W frequency-agile gyrotron. The proposed cavity geometry allows for two operating points, one optimized for frequency agility, and the other for high power. Cavity interaction code simulations show that frequency tunability over a range of 400 MHz can be reached using a smooth transition between the first and second axial mode excitations. In addition, these simulations indicate that up to 7 kW microwave power can be obtained at the high-power operating point. Furthermore, the ohmic load deposited on the walls of the interaction cavity was investigated for high-power operation. The expected microwave power and frequency agility of the cavity are promising for applications such as dynamic nuclear polarization (DNP) spectroscopy and electron paramagnetic resonance (EPR) experiments.