A way granny finally shows lack of interest (6)
I believe the answer is:
apathy
'lack of interest' is the definition.
'a way granny finally' is the wordplay.
'way' becomes 'path' (path is a kind of way**).
'finally' says to take the final letters.
The last letter of 'granny' is 'y'.
'a'+'path'+'y'='APATHY'
'shows' acts as a link.
(Other definitions for apathy that I've seen before include "Impassivity - lack of feeling" , "Disinclination to shift" , "Lack of emotion and interest" , "Indifference, emotionlessness" , "State of listlessness or disinterest" .)