Quick and quiet, sickly on the outside (6)
I believe the answer is:
speedy
'quick' is the definition.
(I know that quick can be written as speedy)
'quiet sickly on the outside' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'sickly' becomes 'seedy' (I've seen this before).
'on the outside' is an insertion indicator.
'p' inserted inside 'seedy' is 'SPEEDY'.
'and' acts as a link.
(Other definitions for speedy that I've seen before include "Quick" , "Express" , "Done quickly" , "in a hurry" , "Moving quickly" .)