The most common and most likely answer to this crossword clue is the 8 plus 4 letter word STRAIGHT FACE
I've seen this crossword clue in The Times
S
T
R
A
I
G
H
T
F
A
C
E
More clues leading to the result STRAIGHT FACE
Buddy explains!
The straight part
We know that "Keep one of these and give nothing away" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case keep one of these and give nothing away = straight face.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.