The goal of this study is to develop a dynamic model for a Carbon Capture (CC) process that can be integrated with a water electrolysis facility. The possibility of operating the post-combustion CC plant dynamically is investigated. The final model successfully tracks the parallel hydrogen production, providing the stoichiometric required CO2 stream for the subsequent methanol reactor. A dynamic model is used to configure controllers and to test the unit performance and stream conditions for various set points. Through the transient operation, the required feed gas is provided while optimizing the solvent and energy requirements. It is found that the slowest acting stage is the reboiler with a time constant of 3.8 h. Other process variables stabilize much quicker, requiring only a few minutes to reach steady-state conditions. The hydrogen-tracking scenario shows that the carbon capture plant can successfully operate under varying conditions with a maximum CO2 output increase of 7% of the minimum flowrate in the representative 24 h simulation time. The output CO2 stream is maintained at the desired >98% purity, 25 °C temperature, and 1.85 bar pressure, which allows to successfully perform hydrogen tracking operations.