The highest-energy known gamma-ray sources are all located within 0 fdg 5 of extremely powerful pulsars. This raises the question of whether ultra-high-energy (UHE;> 56 TeV) gamma-ray emission is a universal feature expected near pulsars with a high spin-down power. Using four years of data from the High Altitude Water Cherenkov Gamma-Ray Observatory, we present a joint-likelihood analysis of 10 extremely powerful pulsars to search for subthreshold UHE gamma-ray emission correlated with these locations. We report a significant detection (> 3σ), indicating that UHE gamma-ray emission is a generic feature of powerful pulsars. We discuss the emission mechanisms of the gamma rays and the implications of this result. The individual environment, such as the magnetic field and particle density in the surrounding area, appears to play a role in the amount of emission.