There are several possible strategies you could use to approach this assignment. The first might be to deconstruct the notion of "relevance". This literary technique involves looking at unstated assumptions, arguing that they are just as important as what is said.
First, you might argue that the point of reading is to broaden your horizons and sympathies by learning about people different than yourself. Thus a story distant in time and culture by its nature helps you achieve that purpose. The very notion of "relevance" suggests that one should live in a bubble, only learning things familiar to you. Making this assumption explicit is a way to deconstruct it.
Next, one could argue that Emily herself shows an interesting evolution of female power from the passive entitlement of the aristocrat to an active role taking charge of her own destiny. As she loses her conventional female beauty she increasingly takes charge of her own life, facing down anyone who wishes to interfere with her and even poisoning the lover who takes advantage of and tries to jilt her. The issue of the relationship of female beauty to power is one not tied to any particular era, despite its specific configuration in the story being localized in the old south.