Her peccadillo aroused a Greek know-it-all (7,6)

I believe the answer is:

delphic oracle

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'a greek know-it-all' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'her peccadillo aroused' is the wordplay.
'aroused' is an anagram indicator (letters roused or stirred up into a new form).
'her'+'peccadillo'='herpeccadillo'
'herpeccadillo' is an anagram of 'DELPHIC ORACLE'.

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