Background: The rapid diffusion of disruptive technologies such as Artificial Intelligence, the Internet of Things, Blockchain platforms, Extended Reality, and Cloud infrastructures is reshaping the digital competence needs of the workforce. While existing frameworks provide useful foundations, they no longer capture the evolving requirements generated by these disruptive forces. This study investigates how exposure to disruptive technologies influences perceived skill gaps, organizational readiness, strategic HR alignment, and employees’ intention to update their skills. Methods: A quantitative survey was completed by 622 employees from Greece, Spain, and Italy, across both public and private sectors. The questionnaire comprised five reflective constructs measured by 24 Likert items: Disruptive Technology Exposure (DTE), Perceived Skill Gaps (PSGs), Organizational Readiness (OR), Strategic HR Alignment (SHRA), and Skill Update Intention (SUI). The proposed model was examined using Partial Least Squares–Structural Equation Modeling (PLS-SEM) with SmartPLS, including assessment of reliability, validity, and predictive power following international guidelines. Results: All four research questions were empirically confirmed. Findings show that exposure to disruptive technologies significantly increases perceived skill gaps (RQ1). These gaps affect organizational readiness to support reskilling (RQ2). Strategic HR alignment mediates the relationship between skill gaps and skill update intention (RQ3). Finally, both perceived skill gaps and organizational readiness have a strong direct impact on employees’ intention to update their skills (RQ4). The structural model demonstrates substantial explanatory and predictive ability, reinforcing the strategic importance of HR in digital transformation. Conclusions: This study concludes that disruptive technologies demand not incremental but strategic reconfiguration of human resource practices. Organizations that align HR policies with technological priorities and invest in readiness for skill updating foster workforces that not only adapt but also create sustained strategic advantage in disruptive contexts.