An apprentice was a novice working in a field to gain experience and skills, in a time called apprenticeship.
Quark served as an apprentice when he was young, working for the District 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 the Ferengi Trade By-Laws, a Ferengi male was required to purchase an apprenticeship from a suitable role model as part of the Ferengi Attainment Ceremony. Based on this, Nog chose to become Benjamin Sisko's apprentice in 2371. (DS9: "Change of Heart")
In 2374, while working with the holographic Leonardo da Vinci to track down stolen equipment, Captain Kathryn Janeway reminded the artist, in an effort to help him accept Janeway's superior knowledge, that he once told her, he was a poor apprentice who could not surpass her master. (VOY: "Concerning Flight")