Fur belonging to me taken by that woman heading off (6)
I believe the answer is:
ermine
'fur' is the definition.
(ermine is a kind of fur)
'belonging to me taken by that woman heading off' is the wordplay.
'belonging to me' becomes 'mine' (I've seen this before).
'taken by' says to put letters next to each other.
'that woman' becomes 'her' (I've seen this before).
'heading off' means to remove the first letter.
'her' with its first letter taken away is 'er'.
'mine' put after 'er' is 'ERMINE'.
(Other definitions for ermine that I've seen before include "'Trimming on royal robes, say (6)'" , "Stoat in its winter coat" , "Animal with brown fur that turns white in winter" , "Fur trimming on royal robes" , "White-coated stoat" .)