Two ensemble simulations of a new Earth system model (ESM) SOCOLv4 (SOlar Climate Ozone Links, version 4) for the period from 2015 to 2099 under moderate (SSP2-4.5) and severe (SSP5-8.5) scenarios of greenhouse gas (GHG) emission growth were analyzed to investigate changes in key dynamical processes relevant for Arctic stratospheric ozone. The model shows a 5–10 K cooling and 5%–20% humidity increase in the Arctic lower–upper stratosphere in March (when the most considerable ozone depletion may occur) between 2080–2099 and 2015–2034. The minimal temperature in the lower polar stratosphere in March, which defines the strength of ozone depletion, appears when the zonal mean meridional heat flux in the lower stratosphere in the preceding January–February is the lowest. In the late 21st century, the strengthening of the zonal mean meridional heat flux with a maximum of up to 20 K m/s (∼25%) in the upper stratosphere close to 70°N in January–February is obtained in the moderate scenario of GHG emission, while only a slight increase in this parameter over 50 N–60 N with the maximum up to 5 K m/s in the upper stratosphere and a decrease with the comparable values over the high latitudes is revealed in the severe GHG emission scenario. Although the model simulations confirm the expected ozone layer recovery, particularly total ozone minimum values inside the Arctic polar cap in March throughout the 21st century are characterized by a positive trend in both scenarios, the large-scale negative ozone anomalies in March up to −80 DU–100 DU, comparable to the second lowest ones observed in March 2011 but weaker than record values in March 2020, are possible in the Arctic until the late 21st century. The volume of low stratospheric air with temperatures below the solid nitric acid trihydrate polar stratospheric cloud (PSC NAT) formation threshold is reconstructed from 3D potential vorticity and temperature fields inside the stratospheric polar vortex. A significant positive trend is shown in this parameter in March in the SSP5-8.5 scenario. Furthermore, according to the model data, an increase in the polar vortex isolation throughout the 21st century indicates its possible strengthening in the lower stratosphere. Positive trends of the surface area density (SAD) of PSC NAT particles in March in the lower Arctic stratosphere over the period of 2015–2099 are significant in the severe GHG emission scenario. The polar vortex longitudinal shift toward northern Eurasia is expected in the lower stratosphere in the late 21st century in both scenarios. The statistically significant long-term stratospheric sulfuric acid aerosol trend in March is expected only in the SSP5.8-5 scenario, most probably due to cooler stratosphere and stronger Brewer–Dobson circulation intensification. Both scenarios predict an increase in the residual meridional circulation (RMC) in March by the end of the 21st century. In some regions of the stratosphere, the RMC enhancement under the severe GHG scenario can exceed 20%.