A very quiet proviso doesn't start show of appreciation (8)
I believe the answer is:
applause
'show of appreciation' is the definition.
(I've seen this before)
'a very quiet proviso doesn't start' is the wordplay.
'very quiet' becomes 'pp' (musical abbreviation for pianissimo).
'proviso' becomes 'clause' (I've seen this in another clue).
'doesn't start' means to remove the first letter.
'clause' with its first letter removed is 'lause'.
'a'+'pp'+'lause'='APPLAUSE'
(Other definitions for applause that I've seen before include "round, perhaps?" , "Clapping US appeal?" , "loud support" , "Gesture of approval" , "big hand" .)