Lack of concern with route passing through outskirts of Aylesbury (6)
I believe the answer is:
apathy
'lack of concern' is the definition.
'route passing through outskirts of aylesbury' is the wordplay.
'route' becomes 'path' ('path' can be a synonym of 'route').
'passing through' is an insertion indicator.
'outskirts of' says to hollow out the word (remove centre letters).
'aylesbury' with its centre taken out is 'ay'.
'path' going inside 'ay' is 'APATHY'.
'with' is the link.
(Other definitions for apathy that I've seen before include "Lack of excitement" , "Lack of interest in things in general" , "Unconcern" , "Detachment" , "Indifference - listlessness" .)