Quiet high-pitched sound associated with English swallow (4,4)
I believe the answer is:
pipe down
'quiet high-pitched sound associated with english swallow' is the definition.
'pipe down' can be an answer for 'quiet' (synonyms). I'm unsure of the 'high-pitched sound associated with english swallow' bit.
'sound associated with english swallow' is the wordplay.
'sound associated' becomes 'pip' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'with' is a charade indicator (letters next to each other).
'english' becomes 'E' (abbreviation).
'swallow' becomes 'down' (I've seen this before).
'pip'+'e'+'down'='PIPE DOWN'
Can you help me to learn more?
(Other definitions for pipe down that I've seen before include "Say no more!" , "Sh!" , "make less noise" , "Be quiet!" , "Shut up!" .)