Problem that confused Rose, on the quiet (5)
I believe the answer is:
poser
'problem' is the definition.
(poser is a kind of problem)
'confused rose on the quiet' is the wordplay.
'confused' is an anagram indicator.
'on' indicates putting letters inside (as in clothing \'on\' a person).
'the quiet' becomes 'p' (music symbol for 'piano'**).
'rose' anagrammed gives 'oser'.
'oser' enclosing 'p' is 'POSER'.
'that' is the link.
(Other definitions for poser that I've seen before include "insincere?" , "Question; one trying to impress" , "Puzzling question for the model" , "This person's affected" , "Difficult problem" .)