In the prey–predator model, predators either hunt their prey or cooperate with them with different strategies. This type of natural phenomenon is observed in different individuals and addresses the many biological key factors among which one of them is hunting cooperation. In the current study, we have considered a Gause-type delayed prey–predator model with hunting cooperation in predators. Here, the delayed prey–predator model with hunting cooperation and density-dependent death rate of predator has not yet been studied. Therefore, we consider a delayed prey–predator system with hunting cooperation. The main focus of this paper is to address how the system stabilized by introducing a discrete time delay into the predator equation. From the literature point of view, destabilization is a common finding that results in most of the prey–predator models, whenever the discrete time delay is induced in the system. For the sake of simplicity, we consider a linear functional response which depends on both prey and predator densities. We also provide the feasible analytical conditions for the coexistence of a steady state. Furthermore, we investigated the stability of coexisting equilibrium points and the existence of Hopf bifurcation is carried out when the delay parameter crosses some critical threshold value say “ \({\tau _0}\) ”. Ecologically, the conclusions section and its numerical simulation also verify the validity of finding analytical results.