The expanding application of artificial intelligence (AI) in human resource (HR) management for competency evaluation reflects organisations' pursuit of efficiency, yet this growth has outpaced the development of essential ethics and governance. This study aimed to determine sectoral differences in perceptions of AI-based evaluation and to develop a tool that balances efficiency with ethics. A small-scale mixed-methods pilot study with professionals in the energy (safety-critical) and education (empathy-based) sectors revealed attitudes differing by sector. While energy practitioners viewed AI as a promising tool for reducing bias in safety analysis, educators were more skeptical, emphasizing challenges around transparency, creativity, and contextual judgment. This paper introduces the Responsible AI Competence Assessment (RAICA) framework to address these governance gaps. RAICA extends the Technology Acceptance Model (TAM) through the addition of ethical trust, algorithmic fairness, and sector-sensitive validation metrics. Furthermore, the framework translates abstract policy instruments into actionable operational protocols, including mandates for bias auditing and algorithmic explainability. The proposed framework provides a flexible and practical governance template for high-stakes decision-making across diverse sectors by bridging efficiency and ethical accountability.