Nap spread out, becoming smoother (9)
I believe the answer is:
sandpaper
'smoother' is the definition.
(I've seen this before)
'nap spread out' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'nap'+'spread'='napspread'
'napspread' with letters rearranged gives 'SANDPAPER'.
'becoming' is the link.
(Other definitions for sandpaper that I've seen before include "Means of smoothing wood" , "Spared pan for the stuff used to prepare surfaces" , "Abrasive substance" , "Abrasive material" , "Smooth" .)