A lip split by a bucket (4)
I believe the answer is:
pail
'a bucket' is the definition.
('pail' can be a synonym of 'bucket')
'a lip split' is the wordplay.
'split' is an anagram indicator.
'a'+'lip'='alip'
'alip' with letters rearranged gives 'PAIL'.
'by' acts as a link.
(Other definitions for pail that I've seen before include "Open-topped container" , "Container; sounds like dim" , "A bucket - the kind Jack and Jill used" , "Cylindrical vessel" , "it may go down well" .)