Puritan, but saucy on the quiet (5)
I believe the answer is:
prude
'puritan' is the definition.
(I know that puritan can be written as prude)
'saucy on the quiet' is the wordplay.
'saucy' becomes 'rude' (I am not sure about this - if you are sure you should believe this answer much more).
'on' means one lot of letters go next to another.
'the quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'rude' put after 'p' is 'PRUDE'.
'but' acts as a link.
Can you help me to learn more?
(Other definitions for prude that I've seen before include "Priggish person" , "Puritan, prig" , "old maid" , "Type overly concerned with decorum" , "may be shocking for me" .)