Musical cycle has style and contemporary sound (8)
I believe the answer is:
ringtone
'contemporary sound' is the definition.
(sound on a mobile phone)
'musical cycle has style' is the wordplay.
'musical cycle has' becomes 'ring' (I can't justify this - if you can you should believe this answer much more).
'style' becomes 'tone' (tone is a kind of style).
'ring'+'tone'='RINGTONE'
'and' is the link.
Can you help me to learn more?
(Other definitions for ringtone that I've seen before include "Sound of modern life" , "Sound heard when someone telephones" , "Sound made by a mobile phone" , "announcement of caller" , "Nitrogen (anag.)" .)