These are the possibilities:
If the volume is held constant:, then the addition of an inert gas has no effect on the equilibrium.
If the volume is allowed to increase (with the addition of an inert gas), the concentrations and the partial pressures, all decrease. The reaction will shift to the left or right depending on the number of moles present on each side.
The change is in the equilibrium and not on the equilibrium constant.
Weather dealing with acid dissociation constant, base dissociation constant, ionic product of water, solubility product or stability constant, at each is constant at a constant temperature.