The catalyst assisted water-splitting method as an eco-friendly and cleaner pathway for energy generation has gained much interest in recent times. In this regard, numerous two-dimensional electrocatalysts such as mono/binary compounds synthesized from group IV, III-V and V elements with compatible activity towards hydrogen evolution, oxygen evolution, oxygen reduction and CO2 reduction have been reported. Motivated by the novel approach of material design and the need for better and cheaper electrocatalytic materials, we have investigated the ground state properties of the GeSb monolayer using state-of-the-art density functional theory. The computed electronic properties reveal the metallic nature of the pristine GeSb monolayer, indicating its potential for utilization as an electrocatalyst. The site-dependent catalytic response of the GeSb monolayer indicates that the Sb-site is more sensitive towards hydrogen adsorption amongst the considered sites. The computed adsorption and Gibbs free energies follow the trend of E < E < E. Finally, we have investigated the role of arsenic (As) and bismuth (Bi) doping on the catalytic activity of the GeSb monolayer. We notice that the electron density modulation occurs at the Sb-site due to incorporation of substitutional doping which results in a 72% enhancement in the catalytic activity of the monolayer on As substitution. The present study envisages that the electron density modulation can be utilized as a pathway for tailoring the catalytic activity of a system for the hydrogen evolution reaction.