The most common and most likely answer to this crossword clue is the 8 letter word REGIONAL
I've seen this crossword clue in The Guardian
R
E
G
I
O
N
A
L
More clues leading to the result REGIONAL
- Criminal or genial local
- A lingo developed after lesson for district
- Local Iron Age construction’s closer to hill
- Bubbly galore in local
- District‘s “number one” in beer coming up
- Territorial lion bursting with rage
- Like some food, best kept by drink on reflection
- Like some food say on island following recipe with bit of lavishness
- Legionary endlessly switching sides in part of country
- Drunk on lager, imbibing one in local
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 = regional.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.
What does REGIONAL mean?
REGIONAL noun- An entity or event with scope limited to a single region.
- Of, or pertaining to, a specific region or district.
- Of, or pertaining to, a large geographic region.
- Of, or pertaining to, one part of the body.
- Of a state or other geographic area, those parts which are not metropolitan, but are somewhat densely populated and usually contain a number of significant towns.