The work is focused on the further development of a regional coupled eco-thermohydrodynamic model of the Arctic seas with the aim of using it to better understand the interaction of dynamic and ecosystem processes in the ocean under a changing climate in the Arctic. We used the MITgcm as a thermohydrodynamic block and an original 7-component ecosystem model which includes the carbon cycle as an ocean biogeochemistry block. The results of a model climatic run for a 40-year modern period for the Arctic shelf region (Kara, Barents and White Seas) are presented. The estimates of the spatial distribution of the chlorophyll-a concentration in the surface layer have clarified the effect of sea ice on primary production in the Arctic seas, including under conditions of a changing climate that leads to a significant reduction of ice cover in the Arctic Ocean. The clear relationship between the area of the marginal ice zone and primary production has been obtained: the moments of their spring-summer peaks coincide completely and they are highly correlated (0.87), proving the importance of this zone in the functioning of the marine ecosystem. As expected, the interannual variability of the integrated primary production and the total sea ice area (both averaged over the hydrological year - from October to September) have demonstrated an antiphase oscillation which means that the reduced sea ice cover area in the previous winter is one of the main reasons for the increase in primary production in the current year.