Partly to rig a migrant craft (7)
I believe the answer is:
origami
'craft' is the definition.
(I have seen 'Japanese craft' mean 'origami' so perhaps 'craft' could also mean 'origami')
'partly to rig a migrant' is the wordplay.
'partly' says the answer is hidden in the clue.
'ORIGAMI' is hidden within 'to rig a migrant'.
(Other definitions for origami that I've seen before include "Art originally created in simple materials to design bird forms" , "Japanese art of folding paper into decorative shapes" , "Making artistic shapes out of paper" , "Paperwork, as it were" , "Jap. paper-folding art" .)