Serial rewritten by one for The National (7)
I believe the answer is:
israeli
'the national' is the definition.
(someone from Israel)
'serial rewritten by one' is the wordplay.
'rewritten' is an anagram indicator.
'by' is a charade indicator (letters next to each other).
'one' becomes 'i' (Roman numeral).
'serial' anagrammed gives 'israel'.
'israel'+'i'='ISRAELI'
'for' is the link.
(Other definitions for israeli that I've seen before include "From Jaffa, perhaps?" , "Native of Middle East state" , "SW Asian" , "Hebrew speaker" , "Inhabitant of Tel Aviv, say" .)