Put off seeing inspector's enthusiasm cut short (7)
I believe the answer is:
disgust
'put off' is the definition.
(thesaurus)
'inspector's enthusiasm cut short' is the wordplay.
'inspector's' becomes 'di's' (abbreviation for Detective Inspector).
'enthusiasm' becomes 'gusto' (gusto is a kind of enthusiasm).
'cut short' means to remove the last letter.
'gusto' with its last letter removed is 'gust'.
'dis'+'gust'='DISGUST'
'seeing' is the link.
(Other definitions for disgust that I've seen before include "Abhorrence" , "contempt" , "'Sicken, revolt (7)'" , "Loathing" , "Nauseate" .)