Turning out to be straying, on the quiet (7)

I believe the answer is:

proving

'turning out' is the definition.
('prove' can be a synonym of 'turn out')

'straying on the quiet' is the wordplay.
'straying' becomes 'roving' ('rove' can be a synonym of 'stray').
'on' is a charade indicator (letters next to each other).
'the quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'roving' after 'p' is 'PROVING'.

'to be' acts as a link.

(Another definition for proving that I've seen is " Showing to be true".)

I've seen this clue in the Evening Standard.

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