Small cover moved smoothly (4)
I believe the answer is:
slid
'moved smoothly' is the definition.
(I've seen this before)
'small cover' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'cover' becomes 'lid' (lid is a kind of cover**).
's'+'lid'='SLID'
(Other definitions for slid that I've seen before include "Slipped" , "Moved smoothly along a surface" , "Moved (eg, on ice)" , "Skidded, slewed" .)