The most common and most likely answer to this crossword clue is the 8 letter word UNCAPPED
U
N
C
A
P
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D
Buddy explains!

The straight part
We know that "Never having been picked" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case never having been picked = uncapped.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 UNCAPPED mean?
UNCAPPED adjective- Not capped (in various senses).
- Not having made an appearance in an international sports match.
- To remove a cap or cover from.
- To take off one's cap.