Island nation's losing a part of Greece (5)
I believe the answer is:
samos
This clue could be a double definition.
'island' is the first definition.
(I've seen this before)
'a part of greece' is the second definition.
(greek island)
'nation's losing' is the link.
I am not very happy about this link. Some or all of it may belong to one of the definitions.
(Other definitions for samos that I've seen before include "Aegean Sea island" , "Greek island?" , "birthplace of Pythagoras" , "somewhere in the Aegean" .)