Jazz music with German backing is in fashion (7)
I believe the answer is:
ragtime
'jazz music' is the definition.
(I've seen this before)
'with german backing is in fashion' is the wordplay.
'with german' becomes 'mit' ('with' in German).
'backing' says the letters should be written backwards.
'is in' means one lot of letters goes inside another.
'fashion' becomes 'rage' (something all the rage is fashionable).
'mit' reversed gives 'tim'.
'tim' put inside 'rage' is 'RAGTIME'.
(Other definitions for ragtime that I've seen before include "Form of jazz with a two-four rhythm" , "Early jazz style" , "Scott Joplin genre" , "Song and dance" , "Type of music" .)