Woman in Missouri shelter mostly the worse for wear (4-5)
I believe the answer is:
moth-eaten
'worse for wear' is the definition.
(damaged by moths)
'woman in missouri shelter mostly' is the wordplay.
'woman' becomes 'thea' ().
'in' indicates putting letters inside.
'missouri' becomes 'mo' (abbreviation for the US state).
'shelter' becomes 'tent' (canvas shelter).
'mostly' means to remove the last letter.
'mo'+'tent'='motent'
'motent' with its final letter taken off is 'moten'.
'thea' put within 'moten' is 'MOTH-EATEN'.
'the' acts as a link.
(Other definitions for moth-eaten that I've seen before include "Old, in bad condition" , "Old and worn" , "Showing severe signs of wear and tear" , "Falling to bits" , "Tatty" .)