The most common and most likely answer to this crossword clue is the 4 plus 2 plus 3 plus 5 letter word NECK OF THE WOODS
I've seen this crossword clue in The Times
N
E
C
K
O
F
T
H
E
W
O
O
D
S
Buddy explains!
The straight part
We know that "district" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case district = neck of the woods.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.