The most common and most likely answer to this crossword clue is the 9 letter word PLAY-OFFS
I've seen this crossword clue in Independent
P
L
A
Y
-
O
F
F
S
Buddy explains!
The straight part
We know that "they may decide promotions (e.g. in football leagues)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they may decide promotions (e.g. in football leagues) = play-offs.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 PLAY-OFFS mean?
PLAY-OFFS noun- A final game in a series needed to break a tie.
- A short series of games to select a league champion.