An apprentice was a novice working in a field to gain experience and skills.
In 2370, Benjamin Sisko referred to his son Jake Sisko as "the new apprentice"' when he reported to Miles O'Brien for his first day at work. (DS9: "Shadowplay") Three years later, in 2375, Jake was again an apprentice, this time at Quark's bar. Quark himself served as an apprentice when he was young, working for a sub-nagus, an experience he ruined by failing to abide by Rule of Acquisition number 112, "Never have sex with the boss's sister." (DS9: "Playing God")
In 2374, while working with the holographic Leonardo da Vinci to track down stolen equipment, Captain Kathryn Janeway reminds the artist, in an effort to help him accept his experiences outside of the holodeck, that he once told her it was a poor apprentice who could not surpass her master. (VOY: "Concerning Flight")