<p>Predator–prey interactions are fundamental to ecological systems, with predator-induced fear increasingly recognized as a key driver of prey dynamics. However, most mathematical models treat fear as static or overlook the interplay between dynamic fear evolution, chemotaxis-driven avoidance, and nonlinear interactions within a rigorous PDE framework. We propose and analyze a novel reaction–diffusion–chemotaxis system incorporating a dynamic fear variable, fear-modulated prey growth and predation rates, and prey chemotaxis away from fear. Using energy estimation and Moser iteration, we establish the global existence and uniform boundedness of classical solutions in two dimensions. We further derive conditions for the existence of a coexistence equilibrium. These reveal a critical threshold that balances prey reproduction, predation efficiency, intraspecific competition, and the fear-mediated effects on growth, predation, and decay. Moreover, local linearization analysis reveals a parameter-dependent instability mechanism near equilibrium, indicating that higher chemotactic sensitivity enhances local stability, whereas global asymptotic analysis exhibits the opposite tendency. This local–global dichotomy highlights the necessity of multiscale analysis in nonlinear systems. Numerical simulations corroborate the theoretical findings, showing that stronger chemotactic sensitivity promotes spatial pattern formation, while intense fear may lead to predator extinction.</p>