The woman who got the hat squashed by a case (6)
I believe the answer is:
sheath
'a case' is the definition.
(I know that case can be written as sheath)
'the woman who got the hat squashed' is the wordplay.
'the woman who' becomes 'she' (I can't explain this - if you can you should give a lot more credence to this answer).
'got' means one lot of letters go next to another.
'squashed' is an anagram indicator.
'hat' with letters rearranged gives 'ath'.
'she'+'ath'='SHEATH'
'by' is the link.
Can you help me to learn more?
(Other definitions for sheath that I've seen before include "cocktail dress" , "Scabbard" , "case for weapon" , "Case for a dagger" , "Cover for a knife" .)