Immune checkpoint inhibitors (ICIs) have revolutionized the treatment of solid malignancies, including non-small-cell lung cancer. However, immunotherapy resistance constitutes a significant challenge. To investigate carbonic anhydrase IX (CAIX) as a driver of resistance, we built a differential equation model of tumor–immune interactions. The model considers treatment with the small molecule CAIX inhibitor SLC-0111 in combination with ICIs. Numerical simulations showed that, given an efficient immune response, CAIX KO tumors tended toward tumor elimination in contrast to their CAIX-expressing counterparts, which stabilized close to the positive equilibrium. Importantly, we demonstrated that short-term combination therapy with a CAIX inhibitor and immunotherapy could shift the asymptotic behavior of the original model from stable disease to tumor eradication. Finally, we calibrated the model with data from murine experiments on CAIX suppression and combination therapy with anti-PD-1 and anti-CTLA-4. Concluding, we have developed a model that reproduces experimental findings and enables the investigation of combination therapies. Our model suggests that transient CAIX inhibition may induce tumor regression, given a sufficient immune infiltrate in the tumor, which can be boosted with ICIs.