Add a very quiet finish (6)
I believe the answer is:
append
'add' is the definition.
(synonyms)
'a very quiet finish' is the wordplay.
'very quiet' becomes 'pp' (musical abbreviation for pianissimo).
'finish' becomes 'end' (come to an end).
'a'+'pp'+'end'='APPEND'
(Other definitions for append that I've seen before include "Add on at the bottom - say signature" , "Add (at the back of a document)" , "provided as add-on" , "Napped (anag)" , "Add (to end of text)" .)