Give the impression of a very quiet listener (6)
I believe the answer is:
appear
'give the impression' is the definition.
'a very quiet listener' is the wordplay.
'very quiet' becomes 'pp'.
'listener' becomes 'ear' (body part which hears or listens).
'a'+'pp'+'ear'='APPEAR'
'of' acts as a link.
(Other definitions for appear that I've seen before include "Seem, look" , "Become visible or seem" , "be published" , "Materialise like ghost" , "Turn up" .)