The safety regulations require periodic reviews of the site hazards when operating nuclear power plants. If any indications of Quaternary fault activity are revealed, the fault displacement hazard should be evaluated. Signs of paleo-liquefaction were recently found at the nuclear site of Paks, Hungary, indicating the late-Pleistocene activity of the fault crossing the site. Except for this, there are no historical or instrumental records of earthquakes at the fault, and the micro-seismic and GPS monitoring results do not indicate activity either. Despite a thorough site investigation of over 40 years, the indications are uncertain and insufficient for defining the fault activity, as required for a probabilistic fault displacement hazard analysis. This paper develops and applies a simplified conservative hazard evaluation method of average fault displacement that allows an in-time decision regarding the safety relevance of the hazard. Geometrical simplification is possible since the fault crosses the site. The fault’s activity is evaluated using magnitude–frequency relations of the area sources developed for probabilistic seismic hazard analysis. The total probability theorem is applied, and different strike-slip fault scaling relations are considered while calculating the probability of non-zero surface displacement, fault rupture length, and average displacement. The fault displacement hazard curve is defined and compared with earlier studies for the same site. Since the late recognition of active faults cannot be excluded at several operating plant sites, the methodology can be applied in the future beyond a single application for the Paks site in Hungary.