The most common and most likely answer to this crossword clue is the 5 plus 4 letter word POKER FACE
I've seen this crossword clue in The Guardian
P
O
K
E
R
F
A
C
E
More clues leading to the result POKER FACE
- Possible straight countenance?
- Somehow cope with freak betraying no emotions
- Zero reading from this dial
- Cope with freak distribution? That gives nothing away!
- Blank stare of female in contest following provocation
- Cope with freak distribution giving nothing away
- Spooner’s people quickly become deadpan
- Fire iron to confront what’s kept straight
- Social network feature female accesses to run unreadable profile
- Novel mostly perfect, okay, except the last bit — it’s hard to read
Buddy explains!

The straight part
We know that "That gives nothing away" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that gives nothing away = poker 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.