In "A Rose for Emily," what kind of conflict is the aldermen's attempt to get Miss Emily pay taxes?

The conflict that this particular situation represents is the external conflict of man vs. society. In this case, it would be Emily versus the changing society of Jefferson County. 

Back in the days when Emily's father, Mr. Grierson, was alive, he and Colonel Sartoris were in friendly terms. When Grierson died, it was generally accepted that the man was a well-known person of influence in the county, albeit not a very well-liked person. Yet,...

The conflict that this particular situation represents is the external conflict of man vs. society. In this case, it would be Emily versus the changing society of Jefferson County. 

Back in the days when Emily's father, Mr. Grierson, was alive, he and Colonel Sartoris were in friendly terms. When Grierson died, it was generally accepted that the man was a well-known person of influence in the county, albeit not a very well-liked person. Yet, for reasons that are still not quite clear, Colonel Sartoris decides to concoct a story that Miss Emily is exempt from paying taxes as a way to repay back money that her father had presumably loaned the county. This is a tale that the townsfolk narrator does not believe. 

Only a man of Colonel Sartoris’s generation and thought could have invented it, and only a woman could have believed it.

As the story says, times did change. Colonel Sartoris died, and the people of Jefferson grew older, taking the place of those who left, and becoming now the new magistrates and aldermen of the town. When they realized that Miss Emily was not paying taxes, they did what any other normal magistrate body would: Go after Emily and demand that her taxes are paid. They had no "hold" or connection to the Griersons. They had no special friendship with Emily's family. Those times of kinship and camaraderie are gone. Emily has to pay her taxes. 

The conflict arises when Emily refuses to acknowledge that ten years have passed since the death of Colonel Sartoris. Moreover, she does not even consider the fact that, as times change, so do rules and regulations. Eternally trapped inside her house, Emily seems to have lost track of time and still insists that she has no taxes in Jefferson. She even tells the aldermen to go see Colonel Sartoris, themselves. 

"I received a paper, yes," Miss Emily said. "Perhaps he considers himself the sheriff . . . I have no taxes in Jefferson."

"But there is nothing on the books to show that, you see We must go by the--"

"See Colonel Sartoris. I have no taxes in Jefferson."

This is a clear conflict between Miss Emily and the society in which she is constrained to coexist with others. She is unable to fit in with society, but she has to try, nevertheless.