The most common and most likely answer to this crossword clue is the 8 letter word SELECTOR
I've seen this crossword clue in The Sunday Telegraph
S
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L
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C
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More clues leading to the result SELECTOR
Buddy explains!

The straight part
We know that "Chooser of players" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case chooser of players = selector.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 SELECTOR mean?
SELECTOR noun- Someone or something which selects or chooses.
- An administrator responsible for selecting which players will play for a side.
- A matching expression in a stylesheet determining which elements in the markup are affected by a style.
- A pointer to a structure describing a segment of memory.
- A text string transmitted to a Gopher server, identifying the resource to be retrieved.
- A disc jockey.