Brought up in sombre district (4)
I believe the answer is:
bred
'brought up' is the definition.
(I've seen this before)
'in sombre district' is the wordplay.
'in' indicates a hidden word.
'BRED' is hidden in the letters of 'sombre district'.
(Other definitions for bred that I've seen before include "Brought forth" , "Gave rise to" , "Engendered" , "Nurtured" , "Procreated" .)