Traps an alternative old Greek (7)
I believe the answer is:
spartan
'old greek' is the definition.
(I've seen this before)
'traps an alternative' is the wordplay.
'alternative' indicates an anagram (an alternative ordering of the letters).
'traps'+'an'='trapsan'
'trapsan' anagrammed gives 'SPARTAN'.
(Other definitions for spartan that I've seen before include "Of conditions, harsh and lacking comforts" , "Lacking luxury, austere" , "Old citizen" , "Strictly disciplined" , "Without comforts" .)