Greek character's caviar announced (3)
I believe the answer is:
rho
'greek character's' is the definition.
(letter from the Greek alphabet)
'caviar announced' is the wordplay.
'caviar' becomes 'roe' (fish eggs).
'announced' indicates a 'sounds like' (homophone) clue.
'roe' is a homophone of 'RHO'.
(Other definitions for rho that I've seen before include "Greek character" , "letter to Athens" , "Greek P" , "Something like 25 [ETA]" , "Gr. letter written as P" .)