Country's abandoning a Greek island as a complete undivided unit (10)
I believe the answer is:
indiscrete
'as a complete undivided unit' is the definition.
(not in discrete parts)
'country's abandoning a greek island' is the wordplay.
I cannot really understand how this works, but
'island' could be 'crete' (Greek island) and 'crete' is found within the answer.
This may be the basis of the clue (or it may be nonsense).
(Other definitions for indiscrete that I've seen before include "Whole" , "Undivided" , "Homogeneous and indivisible (anag of 1 across, 6 and 23)" , "not divided" .)