Move quickly back for jazz? (4)
I believe the answer is:
trad
'jazz?' is the definition.
(trad jazz is a type of jazz)
'move quickly back' is the wordplay.
'move quickly' becomes 'dart' (I've seen this in another clue).
'back' shows that the letters should be reversed in order.
'dart' reversed gives 'TRAD'.
'for' is the link.
(Other definitions for trad that I've seen before include "Type of jazz or folk" , "Conventional (jazz)" , "Style of jazz" , "Form of folk or jazz" , "(Of jazz) traditional" .)