Satie rose regularly to compose melodies (4)
I believe the answer is:
airs
'melodies' is the definition.
('air' can be a synonym of 'melody')
'satie rose regularly' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'satie'+'rose'='satierose'
The alternate letters of 'satierose' are 'AIRS'.
'to compose' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for airs that I've seen before include "Melodies or artificial manners" , "- - and graces" , "Ventilates or tunes" , "Affected manners" , "Ventilates, say grievance" .)