Attach a very quiet conclusion (6)
I believe the answer is:
append
'attach' is the definition.
(appending is a kind of attaching)
'a very quiet conclusion' is the wordplay.
'very quiet' becomes 'pp' (musical abbreviation for pianissimo).
'conclusion' becomes 'end' (something's conclusion is its end).
'a'+'pp'+'end'='APPEND'
(Other definitions for append that I've seen before include "Add (at the back of a document)" , "Napped (anag)" , "provided as add-on" , "Hang on" , "Add, annex" .)