Requests barrels without lids (4)
I believe the answer is:
asks
'requests' is the definition.
('ask' can be a synonym of 'request')
'barrels without lids' is the wordplay.
'barrels' becomes 'casks' ('cask' can be a synonym of 'barrel').
'without lids' means to remove the first letter (I've seen 'without lid' mean this).
'casks' with its initial letter taken off is 'ASKS'.
(Other definitions for asks that I've seen before include "Solicits" , "Puts a question" , "Inquiries" , "Enquires; requests" , "Requests information about" .)