* For a caregiver of infants or young children: A good option would be τροφοφόρος (trophoforos), which literally means "food-bearer" or "nursemaid".
* For a professional nurse (in a hospital setting): There's no direct ancient Greek equivalent. You'd have to use a descriptive phrase, such as ιατρός νοσοκομείου (iatros nosokomeiou), meaning "hospital doctor" (though this would typically refer to a physician). A more accurate but less concise option might be something like γυνή παρασκευάζουσα φάρμακα και φροντίζουσα ασθενείς (gynē paraskeuazousa pharmaka kai phrontizousa astheneis), meaning "woman preparing medicines and caring for patients."
In short, a direct translation isn't possible. The best choice depends heavily on the specific nuance you wish to convey.