Isn't archaic? No, becoming out of date (13)
I believe the answer is:
anachronistic
'out of date' is the definition.
(thesaurus)
'isn't archaic? no becoming' is the wordplay.
'becoming' indicates anagramming the letters.
'isnt'+'archaic'+'no'='isntarchaicno'
'isntarchaicno' is an anagram of 'ANACHRONISTIC'.
(Other definitions for anachronistic that I've seen before include "wrong over dates" , "In false historical context" , "Chronologically misplaced" , "Out of keeping with chronology" , "Of another time" .)