The most common and most likely answer to this crossword clue is the 9 plus 6 letter word GREYHOUND RACING
I've seen this crossword clue in The Times
G
R
E
Y
H
O
U
N
D
R
A
C
I
N
G
Buddy explains!
The straight part
We know that "canine contests" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case canine contests = greyhound racing.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.