Probably the closest thing in antiquity (and up through the early 20th century, actually) would be traveling theater troupes. I'm not aware of any individual troupe gaining such notoriety that they were sought after. It would be more akin to hearing that the circus is coming to town. You don't give a shit who the #1 clown is. You're just excited for the entertainment. But they were noteworthy and discussed in primary sources.

In Classical Greece, you'd get full tragedies, with a four-play festival. But by the end of the Roman Republic, tastes had changed. Much like us, they were keyed into melodrama and gore. So their stage plays would mostly be the juiciest bits pulled from mythology, with lots of tongue-in-cheek jokes. Seneca's Thyestes stands as a great model of that, where his brother cuts up his sons and feeds them to him.

There's an author, Mary Renault, that wrote some thoughtful and insightful historical fiction. One of her works, The Mask of Apollo involves one of these traveling sets.