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Because of their extreme stellar densities, globular clusters are highly efficient factories of X-ray binaries and radio pulsars: per unit of stellar mass, they contain about 1000 times more of these exotic objects. Thus far, 345 radio pulsars have been found in globular clusters. These can be used as precision probes of the structure, gas content, magnetic field, and dynamic history of their host clusters; some of them are also highly interesting in their own right because they probe exotic stellar evolution scenarios as well as the physics of dense matter, accretion, and gravity; one of them (PSR~J0514$-$4002E) might even be the first pulsar - black hole system known. Deep searches with SKA-MID and SKA-LOW will only require one to a few tied-array beams, and can be done during early commissioning of the telescope, before an all-sky pulsar survey using hundreds to thousands of tied-array beams is feasible. Even a conservative approach predicts new discoveries only with the core of SKA-MID AA*, and the full AA* and eventually AA4 is expected to increase the number of discoveries even more, leading to more than doubling the current known population. This offers a great opportunity for early SKAO pulsar science, even before all the collecting area is in place. On the other hand, a more optimistic prediction calls for a 4-5 times growth of the population, leading to a total of about 1700 pulsars to be detectable with SKA-MID AA4 configuration in all Galactic GCs visible by SKA telescopes. Thus, a dedicated search for pulsars in globular clusters will fully exploit the best possible natural laboratories to study many branches of physics and astrophysics, including properties of dense matter, stellar evolution, and the dynamical history of the Galactic globular cluster systems.