Show indifference to quiet carpeting (5)
I believe the answer is:
shrug
'show indifference' is the definition.
(I've seen this before)
'quiet carpeting' is the wordplay.
'quiet' becomes 'sh'.
'carpeting' becomes 'rug' ('rug' can be a synonym of 'carpeting').
'sh'+'rug'='SHRUG'
'to' acts as a link.
(Other definitions for shrug that I've seen before include "Gesture involving the shoulders" , "Shoulder movement to indicate indifference" , "Shoulder movement to show indifference or resignation" , "Gesture of resignation" , "Gesture expressing unconcern" .)