Musical performance on island (4)
I believe the answer is:
gigi
'musical' is the definition.
(I've seen this before)
'performance on island' is the wordplay.
'performance' becomes 'gig' (I've seen this before).
'on' means one lot of letters go next to another.
'island' becomes 'i'.
'gig'+'i'='GIGI'
(Other definitions for gigi that I've seen before include "musical from the 1950s" , "Musical, winner of nine Academy Awards" , "1958 film musical from a Colette novel" , "Lerner and Loewe musical and film" , "Movie" .)