Industrial process safety systems are predominantly reactive: alarms activate after limits are crossed, faults are diagnosed after deviations develop, and HAZOP knowledge remains offline during operation. This paper proposes Predictive Operational Safety Engineering (POSE) as an emerging research paradigm in which operational safety is treated as a continuously forecastable state rather than a post-event classification, shifting the operational question from what has gone wrong? to how much safe operating time remains, and which intervention is most urgent? Four integrated predictive safety metrics anchor the framework: Remaining Safety Margin (RSM), quantifying the normalized distance between the predicted process trajectory and the nearest safety boundary; Remaining Safe Operating Time (RSOT), estimating when that boundary will be crossed under the current trajectory; the Operational Vulnerability Index (OVI), combining margin depletion rate, safeguard availability, and consequence severity into a single intervention-urgency signal; and Predictive Safety Confidence (PSC), the probability that a specific named operator intervention can be executed to completion before the predicted safety boundary is crossed, coupling prediction uncertainty with action execution time. The Predictive Operational Safety Twin (POST) is proposed as a three-layer reference architecture implementing POSE through predictive process intelligence, predictive safety intelligence, and human safety intelligence. The paper synthesizes six research streams, positions POSE against seven adjacent disciplines, states ten guiding principles, and formulates a research agenda. As a conceptual narrative review, the paper does not claim empirical validation of POSE. Instead, it establishes the foundational vocabulary, reference architecture, and research agenda required to advance predictive operational safety from an emerging concept toward benchmarked and industrially validated practice.