The most common and most likely answer to this crossword clue is the 9 letter word HAND-PICK
I've seen this crossword clue in The Times
H
A
N
D
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P
I
C
K
More clues leading to the result HAND-PICK
Buddy explains!

The straight part
We know that "single out specially" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case single out specially = hand-pick.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 HAND-PICK mean?
HAND-PICK verb- To pick or harvest by hand.
- To select carefully and with individual attention.