Popular Chinese island (4)
I believe the answer is:
inch
'island' is the definition.
(inch can mean a small island)
'popular chinese' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'chinese' becomes 'ch' (I've seen this in other clues).
'in'+'ch'='INCH'
(Other definitions for inch that I've seen before include "One 63,360th of a mile" , "Not very far" , "Small measurement unit of distance" , "Progress slowly" , "Non-metric measure" .)