Old lie about banishment (5)
I believe the answer is:
exile
'banishment' is the definition.
(exile is a kind of banishment)
'old lie about' is the wordplay.
'old' becomes 'ex' (prefix meaning former or onetime).
'about' indicates anagramming the letters.
'lie' is an anagram of 'ile'.
'ex'+'ile'='EXILE'
(Other definitions for exile that I've seen before include "Eject from country" , "Person forced from country" , "Displaced person from former French island" , "One banished" , "Person who now lives in another country" .)