Self-reproach about TV detective (7)
I believe the answer is:
remorse
'self-reproach' is the definition.
(synonyms)
'about tv detective' is the wordplay.
'about' becomes 're' (regarding).
'tv detective' becomes 'Morse' (Inspector Morse).
're'+'morse'='REMORSE'
(Other definitions for remorse that I've seen before include "Guilt for a wrong deed" , "Distress from a sense of guilt" , "it may bite" , "display of conscience" , "Contrition for wrongdoing" .)