Clue to an assassination outside the detention centre (4)
I believe the answer is:
hint
'clue' is the definition.
(I know that clue can be written as hint)
'an assassination outside the detention centre' is the wordplay.
'an assassination' becomes 'hit' (as in hit job).
'outside' indicates putting letters inside.
'centre' says to take the centre.
The central letter of 'detention' is 'n'.
'hit' going around 'n' is 'HINT'.
'to' acts as a link.
(Other definitions for hint that I've seen before include "Piece of advice" , "Tip - small amount" , "Tip, clue" , "suspicion" , "Intimate" .)