Pant quietly, after oxygen perhaps (4)
I believe the answer is:
gasp
'pant' is the definition.
('gasp' can be a synonym of 'pant')
'quietly after oxygen perhaps' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'after' means one lot of letters go next to another.
'oxygen perhaps' becomes 'gas' (oxygen is a kind of gas).
'p' put after 'gas' is 'GASP'.
(Other definitions for gasp that I've seen before include "First Greek letter" , "Pant" , "Say "ah"" , "Draw breath sharply" , "Sudden intake of breath" .)