The studies on innovative methods to achieve the maximization of the efficiency and specific power in the fields of energy production and propulsion brought to a modification of the conventional thermodynamic cycles: Pressure Gain Combustors (PGCs) are based on the introduction of new methods of combustion. The conventional and existing turbine configurations show some issues concerning the interaction with PCGs, in particular for Rotating Detonation Engine (RDE): it is necessary to re-design the High Pressure Turbine Stage in order to achieve a greater integration with the unsteadiness of the flow field out of a PGC. During this analysis, the nominal configuration of two conventional turbine vane profiles is considered as the starting point to perform a Numerical Optimization in order to maximise the vane efficiency, ensuring an inlet Mach number not too much far from 0.6.