Earth System Models are routinely used for future projections of the carbon cycle and are by definition simplifications of the real world. The ocean uptake of anthropogenic carbon is to first order a physical-chemical process related to CO2 solubility and ocean circulation. However, changes in biological productivity may affect the ocean carbon cycle and ecosystems in the future under on-going climate change. For example, multiple co-occurring environmental changes act as stressors on the lower trophic levels (phytoplankton, zooplankton) of the ecosystem. To simulate such marine carbon and ecosystem feedbacks, relevant biological processes, so far mostly neglected for the sake of simplicity, need to be considered in the models as well. Here, we present recent developments of the ocean biogeochemistry model REcoM that is also used in the AWI Earth System Model, specifically on the extended representation of zooplankton and on the response of phytoplankton growth to interactive effects of CO2, temperature and light availability. We further present the AWI-ESM results for CMIP6-type future projections in concentration- and emission-driven mode, where we touch upon the variability of air-sea CO2 fluxes in the historical period. Here, we identify atmospheric CO2 growth rate variability as the dominant driver, and highlight important model deficiencies in mixed layer depth trends. Finally, we showcase application examples identifying a weakening of the biological carbon pump in the future Arctic Ocean and on ocean-based negative emission simulations (alkalinity enhancement) with the emission-driven AWI-ESM.