With both knights and wizards, we see squires and apprentices respectively; other versions of this can exist in both fantasy and SF. But this is sometimes not part of a system if it’s private instruction. Being a knight’s squire might have defined expectations and a wizard’s apprentice may not, unless that wizard belongs to a guild that sets forth rules; we have leeway here. These understudies typically live with their master for years, doing menial work and otherwise attending to their master’s professional and even household needs, in addition to receiving instruction. Decide if this makes sense in the setting for any profession. It is more likely when public education is lacking or when someone is an especially sought-after master. It can also be true when the master or subject is evil, for lack of a better word, because it’s unlikely that public education teaches their methods.
Since this is less formal, we may not need to decide at what age apprenticeship can begin, and what duties are expected, what life is like for both master and understudy, and how it ends unless these are standardized. It could be a privileged life of fine dining with powerful people or a miserable one of squalor, suffering, and fear. If the profession is dangerous, this apprenticeship likely is as well. What sort of protection does the master provide, whether physically present or not? What are the benefits beyond the chance to acquire knowledge and skills? Forging personal connections could be a significant attraction, but then it depends on how much respect the apprentice is given. Someone may have had more than one apprenticeship in their past, with wildly different experiences. This is as much a character building as world building issue, other than deciding whether it’s available and for what professions, typically, and whether something like a guild or knighthood establishes guidelines.