Don't go out without your cap? It's a shame (5)
I believe the answer is:
stain
'a shame' is the definition.
(I've seen this in other clues)
'don't go out without' is the wordplay.
'don't go' becomes 'stay' (I've seen this before).
'out' means to remove the last letter.
'without' becomes 'in' (I can't justify this - if you can you should give a lot more credence to this answer).
'stay' with its last letter taken off is 'sta'.
'sta'+'in'='STAIN'
'your cap? it's' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
(Other definitions for stain that I've seen before include "Stigma" , "Discoloured patch" , "Discolour - blemish" , "Spot - shame" , "Discoloured mark" .)