Newspaper fine with subordinate making enormous bloomer (9)
I believe the answer is:
'enormous bloomer' is the definition.
(I know that sunflower is a type of enormous bloomer)
'newspaper fine with subordinate' is the wordplay.
'newspaper' becomes 'sun' (UK newspaper The Sun).
'fine' becomes 'f' (abbreviation e.g. condition of old coins, books).
'with' means one lot of letters go next to another.
'subordinate' becomes 'lower' (synonyms).
'making' acts as a link.
(Other definitions for sunflower that I've seen before include "Plant's" , "seen in Van Gogh's art" , "that Van Gogh used to paint" , "nickname of US State" , "Tall plant" .)