The most common and most likely answer to this crossword clue is the 8 plus 7 letter word ECONOMIC MIGRANT
I've seen this crossword clue in The Guardian
E
C
O
N
O
M
I
C
M
I
G
R
A
N
T
Buddy explains!
The straight part
We know that "an irritation for nationalists" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case an irritation for nationalists = economic migrant.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.