Cool to live without working body part (7)
I believe the answer is:
hipbone
'body part' is the definition.
(I know that leg is part of body)
'cool to live without working' is the wordplay.
'cool' becomes 'hip' (hip can mean cool or fashionable).
'to live' becomes 'be' ('be' can be a synonym of 'live').
'without' indicates putting letters inside ('without' can be similar in meaning to 'outside').
'working' becomes 'on' (on can mean working or activated).
'be' placed around 'on' is 'bone'.
'hip'+'bone'='HIPBONE'
(Other definitions for hipbone that I've seen before include "bit of leg" , "Large part of skeleton" , "One half of the pelvis" .)