Clothing hotel could supply in southwest city not right for Robert? (8)
I believe the answer is:
bathrobe
'clothing' is the definition.
(bathrobe is a kind of clothing)
'in southwest city not right for robert?' is the wordplay.
'in' indicates putting letters inside.
'southwest city' becomes 'bath' (Bath is a city in the southwest of England).
'not right for' becomes 'e' (I can't justify this - if you can you should believe this answer much more).
'robert?' becomes 'rob' (short for Robert).
'bath'+'e'='bathe'
'bathe' placed around 'rob' is 'BATHROBE'.
'hotel could supply' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
(Other definitions for bathrobe that I've seen before include "Towelling dressing gown" , "you may take it after a shower" , "Towelling dressing-gown" , "Towelling garment" , "freshly-washed clothing" .)