Brought up case of renegade, a socialist (6)
I believe the answer is:
reared
'brought up' is the definition.
(rearing is a kind of bringing up)
'case of renegade a socialist' is the wordplay.
'case of' suggests removing the centre (outsides of).
'socialist' becomes 'red' (red is a kind of socialist).
'renegade' with its middle taken out is 're'.
're'+'a'+'red'='REARED'
(Other definitions for reared that I've seen before include "Fostered, brought up" , "Nurtured - rose on hind legs" , "Provided and cared for during childhood" , "Trained" , "Brought up, nurtured" .)