Deep regret about TV inspector (7)
I believe the answer is:
remorse
'deep regret' is the definition.
(I've seen this before)
'about tv inspector' is the wordplay.
'about' becomes 're' (regarding).
'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" .)