Sex god put up between detectives (5)
I believe the answer is:
cupid
'sex god' is the definition.
(Roman god)
'up between detectives' is the wordplay.
'between' is an insertion indicator.
'detectives' becomes 'CID' (abbreviation for Criminal Investigation Department).
'up' placed inside 'cid' is 'CUPID'.
'put' is the link.
(Other definitions for cupid that I've seen before include "Cherubic symbol for love" , "Tiny archer as Roman god of love" , "boy with little bow" , "Roman god of love, child archer" , "godlike figure" .)