Underground hydrogen storage (UHS) has been recognized as a key enabler of the industrial-scale implementation of a hydrogen-based economy. However, the efficiency and storage capacity of hydrogen (H2) in carbonate aquifers can be influenced by the presence of organic acids. Nevertheless, the existing literature contains few investigations of H2/calcite/brine wettability and the influence of organic acids on H2 storability in carbonate reservoirs. Therefore, the present study examines the influence of stearic acid on the dynamic H2/brine wettability of calcite substrates (as a proxy of carbonate formation) under various geological conditions (0.1–20 MPa at 323 K), equilibrated in 10 wt% NaCl brine. In addition, the application of various alumina nanofluid concentrations (0.05, 0.1, 0.25, and 0.75 wt%) is evaluated under the same experimental conditions for enhancing the organic-aged calcite wettability. The results demonstrate a significant impact of stearic acid on the dynamic (advancing and receding) contact angles of the calcite substrates, thereby resulting in a shift from intermediate water-wet to H2-wet conditions, representing an unfavorable state for H2 geological storage. Conversely, the application of alumina nanofluid on the organic-aged calcite substrate enhances the H2/brine/calcite wettability towards an intermediate water-wet state, which is more favorable for H2 residual trapping in carbonate formations. The optimal concentration of alumina nanofluid for the wettability modification of the organically aged calcite samples is found to be 0.25 wt%. These findings highlight the influence of organic acid contamination and the potential of alumina nanofluid application in enhancing H2 geo-storage conditions in carbonate reservoirs.