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Fear can influence the overall population size of an ecosystem and an important drive for change in nature. It evokes a vast array of responses spanning the physiology, morphology, ontogeny and the behavior of scared organisms. To explore the effect of fear and its dynamic consequences, we have formulated a predator-prey model with the cost of fear in prey reproduction term. Spatial movement of species in one and two dimensions have been considered for the better understanding of the model system dynamics. Stability analysis, Hopf-bifurcation, direction and stability of bifurcating periodic solutions have been studied. Conditions for Turing pattern formation have been established through diffusion-driven instability. The existence of both supercritical and subcritical Hopf-bifurcations have been investigated by numerical simulations. Various Turing patterns are presented and found that the change in the level of fear and diffusion coefficients alter these structures significantly. Holes and holes-stripes mixed type of ecologically realistic patterns are observed for small values of fear and relative increase in the level of fear may reduce the overall population size.