Two likely things there is something wrong with the accumulator pressure (if you have one) the pump pressure should be the same as the accumulator. Use a bicycle pressure gauge on the accumulator to check the pressure is the same as the pump. We also found that problem with a faulty pressure switch. Be careful about letting it keep running, if you do the electric motor will burn out, as we found.
I've seen pumps where it's possible to wire them so the pressure switch is out of circuit. May be worth a check?
Otherwise, assuming nothing in the new pump is faulty, the system isn't reaching the required pressure, either because it's emptying your tank into the bilges or water isn't reaching the pump in sufficient quantity to build up the pressure.