Changing stress regimes control fracture network geometry and influence porosity and permeability in carbonate reservoirs. We investigate the impact of stress-regime change on fracture network permeability utilizing outcrop data analysis and a displacement-based linear elastic finite element method. The model is based on fracture networks, specifically, fracture sub-structures. The Latemar, predominantly affected by subsidence deformation and Alpine compression, is taken as an outcrop analogue for isolated (Mesozoic) carbonate buildups with fracture-dominated permeability. We apply a novel strategy involving two compressive boundary loading conditions, constrained by the NW-SE and N-S stress directions in the study area. Stress-dependent heterogeneous apertures and effective permeability were computed by: (i) using the local stress state within the fracture sub-structure and (ii) running a single-phase flow analysis considering the fracture apertures in each fracture sub-structure. Our results show that the impact of the modelled far-field stresses at: (i) subsidence deformation from the NW-SE, and (ii) Alpine deformation from N-S, increased the overall fracture aperture and permeability. In each case, increasing permeability is associated with open fractures parallel to the orientation of the loading stages and with fracture densities. The anisotropy of permeability is increased by the density and connectedness of the fracture network and affected by of shear dilation. The two far-field stresses simultaneously acting within the selected fracture sub-structure at a different magnitude and orientation do not necessarily cancel out each other in the mechanical deformation modelling. These stresses effect the overall aperture and permeability distributions. These effects, which may be ignored in simpler stress-dependent permeability, can result in significant inaccuracies in permeability estimation.