Damage inappropriate to mention in Venice’s unusual promotional activity (5,9)
I believe the answer is:
charm offensive
'promotional activity' is the definition.
'damage inappropriate to mention in venice's unusual' is the wordplay.
'damage' becomes 'harm' ('harm' can be a synonym of 'damage').
'inappropriate to mention' becomes 'off'.
'in' indicates putting letters inside.
'unusual' indicates an anagram.
'harm'+'off'='harmoff'
'venices' is an anagram of 'censive'.
'harmoff' put within 'censive' is 'CHARM OFFENSIVE'.
(Other definitions for charm offensive that I've seen before include "smarmy campaign" , "PR campaign needed" , "Ingratiating campaign is needed" , "Campaign to gain support and become more popular" .)