Drop off slate on the counter (3)
I believe the answer is:
nap
'drop off' is the definition.
(drop off can mean to sleep)
'slate on the counter' is the wordplay.
'slate' becomes 'pan' (both can mean to criticise strongly).
'on the counter' is a reversal indicator (counter can mean in the opposite direction).
'pan' in reverse letter order is 'NAP'.
(Other definitions for nap that I've seen before include "A short sleep or snooze" , "A brief snooze" , "Kip" , "one akin to whist" , "One likely to win" .)