Express indifference by emptying stash onto carpet (5)
I believe the answer is:
shrug
'express indifference' is the definition.
(synonyms)
'emptying stash onto carpet' is the wordplay.
'emptying' suggests removing the centre.
'onto' means one lot of letters go next to another.
'carpet' becomes 'rug' (synonyms).
'stash' with its middle removed is 'sh'.
'sh'+'rug'='SHRUG'
'by' acts as a link.
(Other definitions for shrug that I've seen before include "Gesture expressing unconcern" , "women's wear" , "Momentarily raise the shoulders" , "Express silent doubt" , "indifferent response" .)