A comprehensive assessment of geomechanical risks is essential for the success of geological carbon storage. Although the relationship between injection-induced pore pressure changes and rock failure is broadly understood in poromechanics, the challenge of characterizing and managing geomechanical hazards associated with subsurface CO₂ injection in saline aquifers persists, affecting its viability as a global strategy for achieving a net-zero carbon economy. Here, we investigate the geomechanical response of the Luna saline aquifer in the North Sea to CO₂ injection using coupled compositional flow and geomechanics simulations based on a seismic-driven high fidelity static model. We find a surface uplift of 13 mm following a constant injection rate of 1.5×10⁶ m³/d (i.e., 1 Mt/y) in the Luna aquifer for 20 years, which is considered reasonable and safe for offshore surface facilities. We show that the upper limits of shear stress level (SSL) and tensile stress level (TSL) are 0.5 and 0.78, respectively, in both the reservoir and caprock. Since SSL and TSL values below 0.8 are considered safe, our results suggest that gas injection induced reservoir and caprock failure is unlikely in the study area, providing confidence that caprock mechanical leakage poses a low risk for long-term CO₂ storage.