In this paper, we aim to study the effects of fear of predation in the presence of a competitor species and availability of refuge for the prey population. A discrete-time model of prey–predator–competitor type is formulated to study the dynamical relationship between the interacting species by deriving the conditions for local stability, permanence and existence of Neimark–Sacker bifurcation. A hybrid control technique based on state feedback strategy is implemented to control the chaos in the system. Finally, some numerical simulations are carried out to illustrate the theoretical discussions.