PetroStreet

I was assigned one of the recommendations from HAZOP where the piping design pressure was required to be verified with the pump shut-off pressure, and that was found to be less.
What action could have been carried out in order to make sure that this kind of a findings should not be there?
Has that to do something with HAZOP during design stage?

Yes, this does relate to the design-stage HAZOP, but only partly.
What happened in your case is usually a sign that the basic pressure design basis was not fully aligned early enough between process, mechanical/pump vendor, and piping.
For a centrifugal pump system, the discharge side can see a maximum discharge pressure equal to the maximum suction pressure plus the maximum differential pressure the pump can develop at shut-off. API 610-based guidance and IOGP’s supplementary spec both use that concept for defining maximum discharge pressure.
So if the piping design pressure ended up lower than pump shut-off pressure, the main preventive actions should have happened before or during detailed design, not only after HAZOP.

To ensure these findings don't make it to a HAZOP (where they become expensive "recommendations"), the following actions should be part of the standard design workflow:
Standardize the "Shut-off Rule": Incorporate a design standard that requires P design to be ≥110% (or a similar margin) of the pump shut-off pressure. This should be verified during the P&ID development phase, long before HAZOP.
Coordinate Between Disciplines: Often, the Process Engineer selects the pump, but the Piping Engineer sets the pipe class. A Pump Data Sheet review meeting between Process, Mechanical, and Piping teams ensures everyone is aligned on the maximum possible pressure.
Suction Pressure Accounting: Ensure you are using the maximum possible suction pressure (e.g., from a full tank or a high-pressure upstream header) when calculating shut-off, not just the "normal" operating pressure.

Got that, design phase HAZOP should not be the reference here.
It must have been earlier than that.