Hearing about Violet is unimportant (7)
I believe the answer is:
trivial
'unimportant' is the definition.
('trivial' can be similar in meaning to 'unimportant')
'hearing about violet' is the wordplay.
'hearing' becomes 'trial' (I've seen this before).
'about' is an insertion indicator.
'violet' becomes 'vi'.
'trial' placed around 'vi' is 'TRIVIAL'.
'is' acts as a link.
(Other definitions for trivial that I've seen before include "Worthless" , "Petty, piffling" , "Meaningless" , "Rival it, being unimportant" , "not significant" .)