Person with no future married in Greece (5)
I believe the answer is:
goner
'person with no future' is the definition.
(a 'goner' is doomed or has no future)
'married in greece' is the wordplay.
'married' becomes 'one' (I've seen this in another clue).
'in' means one lot of letters goes inside another.
'greece' becomes 'Gr' (abbreviation).
'one' going within 'gr' is 'GONER'.
(Other definitions for goner that I've seen before include "Person beyond saving" , "Someone beyond any hope of recovery" , "he's bought it" , "Lost cause" , "Person beyond help" .)