The most common and most likely answer to this crossword clue is the 9 letter word DOGFIGHTS
I've seen this crossword clue in The Daily Telegraph
D
O
G
F
I
G
H
T
S
Buddy explains!
The straight part
We know that "contests at a higher level" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case contests at a higher level = dogfights.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 DOGFIGHTS mean?
DOGFIGHTS 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.