Rush up for jazz (4)
I believe the answer is:
trad
'jazz' is the definition.
(trad jazz is a type of jazz)
'rush up' is the wordplay.
'rush' becomes 'dart' (darting is a kind of rushing).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'dart' reversed gives 'TRAD'.
'for' acts as a link.
(Other definitions for trad that I've seen before include "Type of jazz or folk" , "(Of jazz) traditional" , "Form of folk or jazz" , "music" , "Classical (abbr)" .)