Detective's words before meal are degrading (8)
I believe the answer is:
disgrace
'are degrading' is the definition.
(people who disgrace themselves degrade themselves)
'detective's words before meal' is the wordplay.
'detective's' becomes 'di's' (Detective Inspector).
'words before meal' becomes 'grace' (as in saying grace before a meal).
'dis'+'grace'='DISGRACE'
(Other definitions for disgrace that I've seen before include "Shame or loss of respect" , "Cause of shame or dishonour" , "scandal" , "Bring shame upon" , "Dishonour, ignominy" .)