Rose just when music finally finished (8)
I believe the answer is:
ascended
'rose' is the definition.
('ascend' can be a synonym of 'rise')
'just when music finally finished' is the wordplay.
'just when' becomes 'as'.
'finally' indicates one should take the final letters.
'finished' becomes 'ended' ('end' can be a synonym of 'finish').
The final letter of 'music' is 'c'.
'as'+'c'+'ended'='ASCENDED'
(Other definitions for ascended that I've seen before include "R [ROSE]" , "Climbed, went up" .)