Express sadness in public for error (9)
I believe the answer is:
oversight
'error' is the definition.
(oversight is a kind of error)
'express sadness in public' is the wordplay.
'express sadness' becomes 'sigh'.
'in' means one lot of letters goes inside another.
'public' becomes 'overt' ('overt' is associated in meaning with 'public').
'sigh' inserted into 'overt' is 'OVERSIGHT'.
'for' acts as a link.
(Other definitions for oversight that I've seen before include "what supervisor has" , "Lapse" , "Neglect" , "error" , "Shot giver due to unintentional omission" .)