The phrase "to draw an audience" means to attract or gather people to come and watch or listen to something, such as a performance or presentation. Full definition
As noted previously, the text begins with some simple questions that draw the audience into their orbit. (religion-online.org)
Whatever the medium, the opening words or dialogue play a vital role in drawing the audience in so they keep, reading, watching or listening. (elearningindustry.com)
It's off - key, and the lyrics won't draw an audience, but the computer doesn't care. (discovermagazine.com)