Quietly be sick in bucket (4)
I believe the answer is:
pail
'bucket' is the definition.
('pail' can be a synonym of 'bucket')
'quietly be sick' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'be sick' becomes 'ail' ('ail' can be a synonym of 'be sick'**).
'p'+'ail'='PAIL'
'in' is the link.
(Other definitions for pail that I've seen before include "Kind of bucket - ask Jack and Jill" , "Water carrier" , "A bucket - the kind Jack and Jill used" , "Cylindrical vessel" , "Vessel for carrying liquids" .)