Make advances to a very quiet swimmer (8)
I believe the answer is:
approach
'make advances' is the definition.
'a very quiet swimmer' is the wordplay.
'very quiet' becomes 'pp'.
'swimmer' becomes 'roach' (roach is a kind of fish).
'a'+'pp'+'roach'='APPROACH'
'to' is the link.
(Other definitions for approach that I've seen before include "attitude" , "Resemble" , "Come close" , "initial proposal" , "Speak to" .)