Physics question Converting the sea/atmosphere to different states of matter will not affect their mass or the pressure they exert. So the pressure at 1km below the surface would remain roughly the same.

Engineering question I suggest that the best option would be via an underwater tunnel cut from the bottom of the ice sheet (or a bit further down to allow for additional freezing over time). The tunnel should extend horizontally into the continental land mass until it is below a mountain range for insulation purposes. At that point the horizontal tunnel would meet a vertical shaft also filled with water which would rise to a point roughly level with the top of the ice sheet or a bit below.

Water pressure from the liquid ocean would force the water into the tunnel and up the shaft until the point where the column of water in the shaft matched a similar depth of ocean/ice/frozen atmosphere outside. The top of the shaft inside the mountain would be protected from freezing by several km of rock and would also be heated from the interior of the Earth in the same way that deep mines are.

At the top of this water shaft a floating harbour could be constructed with maintenance facilities for the submarines. The floating harbour could be linked to the main habitat by a lift of arbitrary length depending on the safety margin required. The level of floating harbour would change due to tidal influences assuming that the Moon was still in orbit around the Earth at this point and might also change over time in the thickness of the ice changed due to volcanic activity or additional freezing.

In summary no lock gates, no high pressure airlock (if the sea level rose or fell would compress or decompress the air above the shaft a little but the change would be small and easily accommodated) and no pressurised environment.

A high pressure air lock would be the next most suitable solution although as you state it would be subject to failure. Least optimal would be a high pressure environment. In fact a 100 atm pressure habitat would kill the inhabitants.

Physics question Converting the sea/atmosphere to different states of matter will not affect their mass or the pressure they exert. So the pressure at 1km below the surface would remain roughly the same.

Engineering question I suggest that the best option would be via an underwater tunnel cut from the bottom of the ice sheet (or a bit further down to allow for additional freezing over time). The tunnel should extend horizontally into the continental land mass until it is below a mountain range for insulation purposes. At that point the horizontal tunnel would meet a vertical shaft also filled with water which would rise to a point roughly level with the top of the ice sheet or a bit below.

Water pressure from the liquid ocean would force the water into the tunnel and up the shaft until the point where the column of water in the shaft matched a similar depth of ocean/ice/frozen atmosphere outside. The top of the shaft inside the mountain would be protected from freezing by several km of rock and would also be heated from the interior of the Earth in the same way that deep mines are.

At the top of this water shaft a floating harbour could be constructed with maintenance facilities for the submarines. The floating harbour could be linked to the main habitat by a lift of arbitrary length depending on the safety margin required. The level of floating harbour would change due to tidal influences assuming that the Moon was still in orbit around the Earth at this point and might also change over time in the thickness of the ice changed due to volcanic activity or additional freezing.

In summary no lock gates, no high pressure airlock (if the sea level rose or fell would compress or decompress the air above the shaft a little but the change would be small and easily accommodated) and no pressurised environment.

A high pressure air lock would be the next most suitable solution although as you state it would be subject to failure. Least optimal would be a high pressure environment. In fact a 100 atm pressure habitat would kill the inhabitants by nitrogen narcosis and oxygen toxicity