What immediately comes to mind is the piezoelectric effect. I suppose it's enough to devise one possible method, to answer your question "yes."

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/piezo.html

The problem is, though, to achieve a steady flow of power. Like, force alone does not produce work (energy). Force has to be applied over a distance, to do work. Voltage alone, same thing. You need that voltage on a flow of current.

If you deform a piezoelectric crystal, you create a voltage. Now you keep the crystal deformed and steady, run a current between the + and - terminals, and you've drained that energy.

Which says to me that just a constant pressure alone won't convert to energy, even though it can certainly be used to store energy. You can twist that crystal with water pressure, create a voltage, and store energy that way. But then if you want to create a steady flow of power, you have to devise a method to use the stored energy, relieve the pressure on the crystal to create the opposite voltage, and then allow water pressure to again deform the crystal.

There is something wrong in definition “Force alone does not produce work (energy). Force has to be applied over a distance, to do work”.

If a person keeps a heavy object in hands, but does not carry the object from one place to another, he is not doing any work, and we cannot give money for his work. However, our labour relations and understandings is one thing, but processes in physics are entirely different. If we hang a heavy load on nail, set into the wall, under this definition the load does not perform any work because it is in the static state (does not move). However, after some time cracks appear in the wall and later nail pulling out the piece of cement from the wall and the load falls on the floor. The “work is done” and nobody can deny it. The load lying on the floor continues to work under downward gravity pull, but we know nothing and do not want to know anything about this work.

I propose to see the movie https://www.youtube.com/watch?v=bmjBTSdCiVg. You will see John J. Hufford’s Gravity motor (US 6237342 B1 May 29, 2001) in action and in this movie; you can watch how to use a spring force for its conversion into rotary motion-work-energy. In this experiment, the compressed spring spins the wheel acting upon it at an acute tangent angle but the spring itself remains compressed in a static state. It means a force can do work being not applied over a distance.

I think it is possible to find way to convert water pressure to mechanical movement-work-energy.

I am definitely not interested in perpetual motion.

I do not know the work of the norwegian engineers, but I figure that they store energy in the form of compressed air into a tank at high sea deepness. I figure a cylindrical tank with a piston moving in it. Air is compressed to the sea pressure, so that the tank needs not be resistant to pressure. (A simpler way could be to reduce the tank to a plastic balloon, inflated by the compressed air). Compressed air would move a gas turbine to produce energy. Of course, the energy that can be extracted from the compressed air cannot be higher than that applied to compress it. 

As to the submarine, I can imagine that an energy storage can be created by letting seawater at high deepness fill partially a cylinder, so that the air inside is compressed to the sea pressure. The advantage would be to repeat the energy storage at each immersion. I am not so sure it is an efficient device.

Any practical attempts to convert static pressure into energy are interesting and important. I am not talking about perpetual motion. Forget about this definition. I am talking about direct conversion of any force in mechanical movement. Magnet motor (International patent WO2009019001 A3 Apr 30, 2009) that demonstrated at the 41st International Exhibition of Inventions in Geneva (April 10 - 12, 2013), https://www.youtube.com/watch?v=CDpKqdcDDrQ uses energy permanent magnets which creates a powerful attractive/repulsive force of these permanent magnets. This force causes the rotor in motion. The rotor of this motor rotates at 2600 rpm using permanent magnets only. A perpetual motion machine is a hypothetical machine that can do work indefinitely without an energy source https://en.wikipedia.org/wiki/Perpetual_motion. You see now this motor is not a perpetual motion machine. The author of patent WO2009019001 A3 invented a way to convert attractive/repulsive force of permanent magnets into rotary motion.

The Yildiz machine looks very similar to all attempts of perpetual motion.

It stopped after 4,5 hrs, a proof that its motion is not perpetual; so it exploited some internally stored form of energy., because it is definitely proved that any production of energy must exploit and convert some other form of energy.

But the machine exhibited in Geneva had nothing to do with norwegian inventors. Can you kindly give any reference to, or description of their idea ?

I am sorry. I cannot help you to understand what I am talking about. I think somebody will be able to help you. I want just to say; if the existence of such natural forces as gravity force, the spring force and the attractive/repulsive force of permanent magnets is an absolute fact means, there are sources of energy which actuate this forces in action. You can see lots of models in operation because of these energies. Think about it. Water pressure in the ocean has own source of energy. It is gravity. I do not blame that modern science knows nothing about these sources of energy.

The answer to the question how to convert the water pressure on submarine in energy, so necessary for a submarine you will find in article https://www.researchgate.net/publication/298045558_Method_for_converting_gravity_force_spring_force_and_force_of_permanent_magnets_in_a_rotary_motion

Article Method for converting gravity force, spring force and force ...

After my answer I thought a little and I decided that exploiting the seawater pressure to save energy can be done more simply.

It is enough to pump air (at the pressure existing at the selected deepness) into an insulated cavity where insulation prevents air escaping; only the cavity roof should be insulated.

The compressed air is umped or drawn through a tube, and the energy would be supplied to compressed air and extracted by expanding it, in a piston machine acting as a compressor/expander at the shore.

I think this is the simplest way to store energy.

If a submarine cavity is not reliable (or is not tight), it could be replaced by a flexible sack laying on sea bottom.

I only referred to the idea reported by Vladimir, of using deep sea pressure to store energy (not to produce it, of course).

It is symmetrical to the idea of storing energy with water raised at higher altitude, as it is often done. If that cannot be done when mountains are lacking, compressed air under deep water could be interesting (and less expensive).

You can't extract energy from a static field, or from static pressure, without moving a mass (or a charge). Water pressure can be used to spin a turbine, compress a gas or deform a spring (or piezoelectric material), but something has to move, and you can't un-move it without expending at least as much energy as you just extracted.  On a submarine, any scheme you devise to extract energy from external hydrostatic pressure must involve allowing the water to move to a region of lower pressure - and the only such region is inside the submarine.  You lose buoyancy as you take on the water, which is rather a serious problem on a sub, and you can't pump the water back out without expending more energy than you initially extracted.

One could tow or carry an external tank, let water into it while extracting energy, and then discard the tank.  Changes in buoyancy would be a major inconvenience, but for a stationary installation such a tank could, in theory, serve as a power source.  However, I suspect you'd get a lot more energy, at lower cost, from a simple battery.