Who manages to trap island parrot? (6)

I believe the answer is:
copier
'parrot?' is the definition.
(thesaurus)
'who manages to trap island' is the wordplay.
I cannot quite understand how this works, but
'island' could be 'i' (geographical abbreviation) and 'i' is present in the answer.
The remaining letters 'coper' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for copier that I've seen before include "Machine for making duplicates" , "Machine to reproduce print" , "Something that duplicates" , "Duplicator" , "Machine for making facsimiles" .)