Shrewd woman passing through the outskirts of Coventry (5)
I believe the answer is:
canny
'shrewd' is the definition.
(both can mean having good judgement)
'woman passing through the outskirts of coventry' is the wordplay.
'woman' becomes 'ann' (woman's name).
'passing through' indicates putting letters inside.
'the outskirts of' suggests removing the centre (only letters on the outskirts).
'coventry' with its centre removed is 'cy'.
'ann' put into 'cy' is 'CANNY'.
(Other definitions for canny that I've seen before include "Worldly-wise" , "Shrewd, knowing" , "Shrewd like Scotsman" , "Shrewd, clever" , "Astute" .)