Softly pull the stopper (4)
I believe the answer is:
plug
'the stopper' is the definition.
('plug' can be a synonym of 'stopper')
'softly pull' is the wordplay.
'softly' becomes 'p' (short for piano, musical term for softly).
'pull' becomes 'lug' (I've seen this before).
'p'+'lug'='PLUG'
(Other definitions for plug that I've seen before include "Piece of tobacco; block" , "Piece of publicity" , "Good word" , "Publicise -- stop" , "Stuff" .)