Nae means no or not in Scottish dialect. The clue "Dundee denial" refers to the usage of the term "nae" as a way of denying or rejecting something in the dialect spoken in Dundee, Scotland.
Note: The provided meaning of the answer is for the latest New York Times crossword puzzle clue: Burnsian lead-in to body. Explanations are generated by AI and may be inaccurate.