He has to live at the detention centre (3)
I believe the answer is:
ben
'he' is the definition.
(I've seen this in another clue)
'to live at the detention centre' is the wordplay.
'to live' becomes 'be' ('be' can be a synonym of 'live').
'at' is a charade indicator (letters next to each other).
'centre' means to look at the middle letters.
The middle letter of 'detention' is 'n'.
'be'+'n'='BEN'
'has' acts as a link.
(Other definitions for ben that I've seen before include "High mountain (Scots)" , "inner room in Oban, say" , "A Big London clock tower" , "& 3 Across Epic film" , "Mountain; man's name" .)