Medical breakthrough (4)
'medical breakthrough' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for cure that I've seen before include "Heal or preserve" , "Make healthy, preserve" , "Make better - smoke" , "Remedy, therapy" , "Make well again" .)
(Other definitions for curve that I've seen before include "Comparable in some respects" , "Line that isn't straight" , "small bulge" , "Arch" , "Gentle bend, arc" .)