The most common and most likely answer to this crossword clue is the 3 plus 9 plus 3 letter word THE FALKLANDS WAR
I've seen this crossword clue in The Guardian
T
H
E
F
A
L
K
L
A
N
D
S
W
A
R
Buddy explains!
The straight part
We know that "fighting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fighting = the falklands war.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.