GI's Island movements in rapidly executed series of notes (9)
I believe the answer is:
glissandi
'series of notes' is the definition.
(I've seen this before)
'gi's island movements' is the wordplay.
'movements' is an anagram indicator (I've seen 'movement' mean this (letters move around)).
'gis'+'island'='gisisland'
'gisisland' with letters rearranged gives 'GLISSANDI'.
'in rapidly executed' acts as a 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 glissandi that I've seen before include "playing, while sliding up and down the passages" , "Slides (music)" , "Series of rapidly ascending or descending musical notes" , "Players may perform them" , "showing smooth actions" .)