Female with an obsession for covering things up (9)

I believe the answer is:

sheathing

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'covering things up' is the definition.
I can't judge whether this defines the answer.

'female with an obsession' is the wordplay.
'female' becomes 'she' (I've seen this before).
'with' is a charade indicator (letters next to each other).
'an' becomes 'a'.
'obsession' becomes 'thing' (I've seen this before).
'she'+'a'+'thing'='SHEATHING'

'for' is the link.

Can you help me to learn more?

(Other definitions for sheathing that I've seen before include "putting it in a case" , "protective covering" .)

I've seen this clue in the Evening Standard.

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