Wow, all these responses and yet the OP has not properly described what they mean by "undersized motor", or even what type of pump it is!
ASSUMING that it is a centrifugal pump with a fixed speed motor (no VFD), the motor is only undersized IF the desired operating FLOW is above the flow at which the motor's design power is reached. It's the flow that matters, not the pressure, and the flow is determined by the frictional loss of the system. If the frictional losses of the system are such that the pump cannot generate enough head to cause that much flow, then the motor is not undersized for that duty. Some people think you must always size a pump's driver for "full run-out", meaning the flow you would get with a flooded suction with no frictional loss and a fully open discharge, i.e. operating the pump to the far right hand side of the head/flow curve, well to the right of BEP. That is definitely not always the case!
Large pumps start to have durability problems if not operated close to their best efficiency point, and of course you want that anyway because they consume a lot of power. But smaller pumps (say less than 10 hp) are often run nowhere near their BEP for their entire lives- often far to the left of the BEP at a high head, low flow and hence low power case, and as long as their minimum flow is met, they do so without significant ill effect unless something else (cavitation, surging etc.) is causing the damage.
If the motor is operated beyond that max driver power (flow) point, it will pull more current than it is allowed in design, and in a properly designed system the motor will trip the overload.