Eye part of Emerald Isle, briefly (4)
I believe the answer is:
iris
'eye part' is the definition.
(iris is a part of the eye)
'emerald isle briefly' is the wordplay.
'emerald' becomes 'ir' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'isle briefly' becomes 'is' (geographical abbreviation; 'briefly' indicates an abbreviation).
'ir'+'is'='IRIS'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for iris that I've seen before include "Pupil is at the centre of this" , "Pupil's place?" , "bloomer?" , "is 21[WOMAN], perhaps" , "pupil's governor" .)