Function (police social) raised slightly less than half (5)
I believe the answer is:
cosec
'function' is the definition.
(mathematical function)
'police social raised slightly less than half' is the wordplay.
'slightly less than half' indicates a hidden word (hidden in less than half of the letters).
'raised' shows that the letters should be reversed in order (going up in a down clue).
'cesoc' can be found hidden inside 'police social'.
'cesoc' in reverse letter order is 'COSEC'.
(Other definitions for cosec that I've seen before include "Inverse of sine (abbr.)" , "(In mathematics) the reciprocal of sine (abbr)" , "company secretary" , "(In maths) reciprocal of sine (abbr)" , "Trig function" .)