Regret about detective (7)
I believe the answer is:
remorse
'regret' is the definition.
(remorse is a kind of regret)
'about detective' is the wordplay.
'about' becomes 're' (regarding).
'detective' becomes 'morse' (I've seen this before).
're'+'morse'='REMORSE'
(Other definitions for remorse that I've seen before include "Pity" , "Guilt for a wrong deed" , "Self-reproach" , "Ruefulness" , "Distress from a sense of guilt" .)