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A leak test or leakeage exam is a visual examination for indication of leakage conducted during the hydrostatic test. Once the pressure retaning boundry has been pressuruzed to the required pressure, stabilized, and the required hold time has elapsed, the visual examination begins. ASME Sect. XI (for example) allows for the exam to be conducted with or without the removal of insulation. Look for leakage or signs of leakage over the entire boundry, and any areas beneath the pipe or vessel. Any leakage should be reported and quantified if possible, even leakage where it is expected such as valve packing .
As LynLynch said; the hydro should be performed in acccodance the the applicable code or standard. I used Sect XI for example only.