Important American soldier returned after onset of battle (3)
I believe the answer is:
big
'important' is the definition.
('big' can be a synonym of 'important')
'american soldier returned after onset of battle' is the wordplay.
'american soldier' becomes 'gi' (**).
'returned' says the letters should be written backwards.
'after' is a charade indicator (letters next to each other).
'onset of' says to take the initial letters.
The initial letter of 'battle' is 'b'.
'gi' reversed gives 'ig'.
'ig' put after 'b' is 'BIG'.
(Other definitions for big that I've seen before include "Massive" , "Circus tent" , "Of considerable size" , "Huge" , "London bell" .)