Venetian lover's first, tragic sweetheart (9)
I believe the answer is:
valentine
'sweetheart' is the definition.
(valentine is a kind of sweetheart)
'venetian lover's first tragic' is the wordplay.
'first' says to take the initial letters.
'tragic' indicates an anagram.
The initial letter of 'lovers' is 'l'.
'venetian'+'l'='venetianl'
'venetianl' anagrammed gives 'VALENTINE'.
(Other definitions for valentine that I've seen before include "February lover" , "Saint of sweethearts" , "Card to sweetheart" , "A loving greeting card sent on February 14th" , "Message for February 14" .)