A Nanny is a person who looks after a family's child or children in the family's home in place of the parents. Sometimes referred to as a nurse, the position existed in a number of cultures throughout the galaxy, usually amongst the upper classes of a society.
Trelane's parents hired a nanny during the 23rd century to look after him after his first encounter with the USS Enterprise. Trelane was able to escape briefly and capture several Federation starships in the process before his nanny found him and took him away. (TOS video game: Judgment Rites)
The position also existed in Klingon society. In the House of Mogh, a woman known as Kahlest was hired by Mogh, son of Worf and his wife Kaasin to look after their sons Worf and Kurn. Kahlest accompanied Mogh, Kaasin, and Worf to Khitomer and was one of the few to survive the Romulan attack on the outpost. (TLE novel: The Art of the Impossible and TNG episode: "Sins of the Father")
Captain Kathryn Janeway, during the first year that the USS Voyager was stranded in the Delta Quadrant, played a holographic program in which she played the role of Mrs. Davenport, a nanny to the children of a wealthy man whose wife had died some time ago. (VOY episode: "Learning Curve")