<p>Selective harvesting is a vital strategy for managing over-exploitation and preventing the incidental killing of juvenile species. A specific time delay should be maintained during harvesting activities to ensure that the species reach a certain age or size threshold, commonly known as harvesting-induced delay. Also, predator-induced fear may reduce the reproduction rate of prey species, and the effect of this indirect interaction can extend into subsequent seasons or generations. The present work highlights the role of harvesting-induced delay and gestation delay of a generalist predator, with its fear and carry-over effects in prey species. We use Crowley-Martin functional response to represent the per capita consumption rate of predator on the prey population. We analyzed both non-delay and delay cases of the model analytically and identified various local bifurcations such as Hopf, saddle-node and transcritical bifurcations. The geometric method of crossing curves is used to determine possible threshold values in two-delay parameter plane at which Hopf bifurcation may occur. Numerical findings reveal that a significant level of fear in prey and moderate harvesting of predator support stable coexistence of both species. Under constant harvesting effort, the harvesting-induced delay leads to five scenarios: instability invariance, stability change, instability switching, stability invariance and stability switching. However, the harvesting effort causes stability switching and stability change with fixed harvesting delay. We obtained that the model system becomes sensitive to both gestation delay and selective harvesting in predator, which can either support or disrupt the stable coexistence of species. The dynamics influenced by harvesting-induced delay, fear, and gestation delay display intricate patterns, offering insights into ecological harmony.</p>