Monolayer germanium sulfide (GeS) has gained significant attention for its exceptional anisotropic electronic conductance, notable excitonic effects, and wide range of applications. In this study we used density functional theory, the nonequilibrium Green's function, and many-body perturbation theory to investigate electronic transport properties and exciton radiative lifetime of single-layer germanium sulfide. Our theoretical findings showed that applying up to 8% compressive strain yielded a nearly threefold increase in carrier mobility and dramatically enhanced device's current intensity. Moreover, we observed that strain engineering allowed for fine-tuning of the electron-hole recombination time. At 6% tensile strain, the effective radiative lifetime was as short as 0.81 ps, which is 4 times faster than the intrinsic case and 24 times faster than at 8% compressive strain. These results highlight the potential of strain engineering to customize the electronic and optical properties of GeS monolayer for specific electronic, optoelectronic, and photovoltaic applications.