Style of music unknown in support of The Cure? (7)
I believe the answer is:
therapy
'cure?' is the definition.
(cure is a kind of therapy)
'style of music unknown in support of the' is the wordplay.
'style of music' becomes 'rap' (I've seen this before).
'unknown' becomes 'y' (algebra).
'in support of' means one lot of letters go next to another (in a down clue, some letters hold up others).
'rap'+'y'='rapy'
'rapy' put after 'the' is 'THERAPY'.
(Other definitions for therapy that I've seen before include "will do you good" , "Treatment designed to cure illness or disability" , "Curative treatment" , "Remedial treatment" , "Medical treatment" .)