Deep regret about TV inspector (7)
I believe the answer is:
remorse
'deep regret' is the definition.
(I've seen this in another clue)
'about tv inspector' is the wordplay.
'about' becomes 're' ('re' means regarding or about).
'tv inspector' becomes 'morse' (I've seen this before).
're'+'morse'='REMORSE'
(Other definitions for remorse that I've seen before include "display of conscience" , "compassion" , "A feeling of deep regret" , "Compunction" , "Feeling of guilt" .)