Answer:
The answer to the question: During the medieval period, which group played an important role in staging plays in various parts of towns, would be, the trade guilds.
Step-by-step explanation:
Because a guild, like the trades guild, is an organization of craftsmen who are responsible for overseeing the application of their craft, or their activity, in specific areas, it fell under their tutelage to also become responsible for the setting of plays that would be offered to the public in different parts of a town. The first guilds ever created were of tradesmen and they became really important as an organization of specialized people in different areas.
In theater, as mentioned before, these guilds would have the necessary tools and people to build up the stages, and move them from place to place, and under the tutelage and authorization of a monarch, or ruler, they would set up the plays.