The most common and most likely answer to this crossword clue is the 8 letter word DOGFIGHT
I've seen this crossword clue in The Daily Telegraph
D
O
G
F
I
G
H
T
More clues leading to the result DOGFIGHT
- Follow key number, heading off for battle
- Tussle … between boxers?
- Clash between boxers? Scrap that's up in the air
- Encounter that’s not just pettish?
- Shadow boxing, a contest between fighters?
- Conflict in the air, a clash between setters, perhaps
- Clash between boxers perhaps that Sky would stage?
- In which boxers do combat?
- Heightened clash of brawling boxers, say
- Conflict between setters, say — in which one may be shot down
Buddy explains!

The straight part
We know that "Conflict in the air" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case conflict in the air = dogfight.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 DOGFIGHT mean?
DOGFIGHT noun- A twisting turning battle between two or more military aircraft, especially between fighters.
- A fight between dogs.
- To engage in a battle between fighter planes.