Between extremes of courtesy, a woman is businesslike (5)
I believe the answer is:
canny
'businesslike' is the definition.
Both the definition and answer are adjectives. Maybe you can see an association between them that I can't see?
'between extremes of courtesy a woman' is the wordplay.
I cannot really see how this works, but
'a' could be 'an' and 'an' is present in the answer.
This may be the basis of clue (or it may be nonsense).
'is' acts as a link.
Can you help me to learn more?
(Other definitions for canny that I've seen before include "Shrewd, clever" , "Fly" , "Worldly-wise" , "Shrewd like Scotsman" , "Astute" .)