Apprenticeship, "a system of training a new generation of practitioners of a skill," may be appropriate.
Dues-paying also is used. Examples from link: "He spent his dues-paying years as a cocktail pianist. ... She had many years of dues-paying before her abilities were recognized."
Another relevant phrase, albeit not a single word, is honing his or her craft. Examples are easily found on the web. For example, journalnow.com writes in a headline, "Honing his craft on stage and screen: Michael Shannon is selected as RiverRun’s Emerging Master for 2011" and in the second half of the article lists Shannon's stage experience, from high school forward.
Note, for any of these terms, you might have to add "arduous" or "travail-filled" in front, or work in "seasoned veteran", if you want to indicate much hard work was involved.