Author arguing about ladies, primarily (7)
I believe the answer is:
rowling
'author' is the definition.
(JK Rowling)
'arguing about ladies primarily' is the wordplay.
'arguing' becomes 'rowing' (I've seen this before).
'about' means one lot of letters goes inside another.
'primarily' says to take the initial letters.
The first letter of 'ladies' is 'l'.
'rowing' placed around 'l' is 'ROWLING'.
(Other definitions for rowling that I've seen before include "Harry Potter's creator" , "J K - - (writer)" , "J. K, author of Harry Potter stories" .)