The test for whether a tradition has clergy is not whether it has professionals, buildings or authority. It is whether some act is reserved to a class of people who were formally made into that class.
By that test the traditions divide unevenly.
Catholic and Orthodox Christianity have clergy in the fullest sense. Only a priest may consecrate the Eucharist and pronounce absolution; only a bishop may ordain. These are not efficiencies or conventions. The tradition holds that an unordained person attempting them does not do them badly but does not do them at all.
Judaism does not, and this surprises people constantly. A rabbi is a teacher and an authority on law, ordained in the sense of being certified competent to rule on questions. Nothing is reserved to him. A layperson may lead prayer, read the Torah, conduct a marriage, and perform a burial. The priestly caste that did have exclusive ritual functions lost them when the Temple was destroyed, and what survives of it is a set of minor honours and restrictions attaching to descent.
Islam has no ordination at all. An imam leads prayer and is simply whoever is best qualified among those present; any adult male may do it. The ulama, the scholars, are trained, credentialed and enormously influential, and no rite makes them what they are. Shia Islam's clerical hierarchy is a partial exception in social fact and still not an ordained priesthood.
Buddhist monks are ordained but are not clergy in the mediating sense. A monk does not stand between a layperson and anything. What he offers is a field of merit, teaching, and an example, and the ordination confers a discipline rather than a power.
Protestant Christianity varies across its whole range, from churches with a strong ordained ministry to those where the pastor's authority is functional and revocable by the congregation that called him.
The word is Western and Christian in origin. It should be checked against a tradition before being used of it, not assumed to fit.