Dispensation (noun):
(1) a: a general state or ordering of things; specifically: a system of revealed commands and promises regulating human affairs
b: a particular arrangement or provision especially of providence or nature
(2) a: an exemption from a law or from an impediment, vow, or oath
b : a formal authorization (Merriam-Webster)
Found on Page I, Paragraph 3 of “A Rose for Emily”–>“Alive, Miss Emily had been a tradition, a duty, and a care; a sort of hereditary obligation upon the town, dating from that day in 1894 when Colonel Sartoris, the mayor–he who fathered the edict that no Negro woman should appear on the streets without an apron-remitted her taxes, the dispensation dating from the death of her father on into perpetuity.”
I believe the word in this quote means that Colonel Sartorise exempted Miss Emily from paying taxes because her father was once seen as a person of prestige aristocratic upbringings.
I think you’ve gotten the definition correct, that Miss Emily was exempt from paying taxes, but the reason isn’t right. Could you look back at the passage to figure out what’s going on there? Remember that the long dash is often used to include an aside or a parenthetical comment. That might help you get a better sense of the flow of the sentence. You can edit your post by clicking EDIT on the line below your post title.