Doing wrong to storm after her, heading off (6)
I believe the answer is:
errant
'doing wrong' is the definition.
(I've seen this before)
'storm after her heading off' is the wordplay.
'storm' becomes 'rant' (both can mean to rage).
'after' means one lot of letters go next to another.
'heading off' means to remove the first letter.
'her' with its initial letter taken away is 'er'.
'rant' put after 'er' is 'ERRANT'.
'to' acts as a link.
(Other definitions for errant that I've seen before include "looking for adventure" , "Quixotic" , "Root vegetable" , "Wandering (as a knight?)" , "Behaving badly" .)