Reducing cold water pressure for a shower.

I’m guessing your cold water is at mains pressure and your hot is gravity fed from the tank above, you would need to install a pump on the hot water from the tank above so that the hot and cold are equal pressure

The answer is yes Modern shower’s thermostatic or not work on high pressure so not suitable for unbalanced pressure A few showers have manual impellers that the cold water will use to increase the hot water to give a better shower Trevi is one name I remember Obviously you can change your low pressure hot water cylinder for a main’s pressure cylinder but far more expensive Regards Dave

Other than a pump on the hot you could run a new pipe to the cold feed from the hot water header tank but when you make the new hole in the header tank make sure it's lower if possible then the cold feed pipe to the cylinder that way if ever there was a problem with the water supply filling the header tank and you was in the shower at the time then the hot would run out first making sure there is no chance of you scolding yourself and this way both pressure would be the same.

You can replace the shower with a thermostatic shower this would adjust the temperature automatically/possibly a pressure reducing Valve if cold is mains pressure