The woman with an obsession offering protection (9)
I believe the answer is:
sheathing
'protection' is the definition.
(I know that sheathing is a type of protection)
'the woman with an obsession' is the wordplay.
'the woman' becomes 'shea' ().
'with' means one lot of letters go next to another.
'an obsession' becomes 'thing' (as in 'having a thing' for someone or something).
'shea'+'thing'='SHEATHING'
'offering' acts as a link.
(Other definitions for sheathing that I've seen before include "protective covering" , "putting it in a case" .)