The most common and most likely answer to this crossword clue is the 9 letter word RIVALRIES
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Buddy explains!

The straight part
We know that "competitions" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case competitions = rivalries.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 RIVALRIES mean?
RIVALRIES noun- An ongoing relationship between (usually two) rivals who compete for superiority.
- The characteristic of being a rivalrous good, such that it can be consumed or used by only one person at a time.
- Any competition between two or more things or factors.