Unavoidable death of obese European (4)
I believe the answer is:
fate
'unavoidable death' is the definition.
'obese european' is the wordplay.
'obese' becomes 'fat' (similar in meaning).
'european' becomes 'e' (abbreviation e.g. EU).
'fat'+'e'='FATE'
'of' acts as a link.
(Other definitions for fate that I've seen before include "E.g. Clotho, Atropos" , "Inevitable destiny" , "Final issue" , "Fortune" , "Predestination" .)