Near a very quiet insect (8)
I believe the answer is:
approach
'near' is the definition.
(synonyms)
'a very quiet insect' is the wordplay.
'very quiet' becomes 'pp' (musical abbreviation for pianissimo).
'insect' becomes 'roach' (roach is a kind of insect).
'a'+'pp'+'roach'='APPROACH'
(Other definitions for approach that I've seen before include "Come near - means of access" , "driveway" , "initial proposal" , "follows drive" , "Drae near" .)