Within the framework of many-body perturbation theory integrated with density functional theory (DFT), a novel defect-subspace projection GW method, the so-called p-GW, is proposed. By avoiding the periodic defect interference through open boundary self-energies, we show that the p-GW can efficiently and accurately describe quasi-particle correlated defect levels in two-dimensional (2D) monolayer MoS₂. By comparing two different defect states originating from sulfur vacancy and adatom to existing theoretical and experimental works, we show that our GW correction to the DFT defect levels is precisely modelled. Based on these findings, we expect that our method can provide genuine trap states for various 2D transition-metal dichalcogenide (TMD) monolayers, thus enabling the study of defect-induced effects on the device characteristics of these materials via realistic simulations.