Astute woman in outskirts of Coventry (5)
I believe the answer is:
canny
'astute' is the definition.
(I've seen this before)
'woman in outskirts of coventry' is the wordplay.
'woman' becomes 'ann' (woman's name).
'in' means one lot of letters goes inside another.
'outskirts of' says to hollow out the word (remove centre letters).
'coventry' with its middle taken out is 'cy'.
'ann' put within 'cy' is 'CANNY'.
(Other definitions for canny that I've seen before include "Fly" , "Shrewd, knowing" , "Shrewd, clever" , "Shrewd like Scotsman" , "Astute" .)