If you give nothing away you conceal or avoid revealing secret information or refrain from giving clues about your emotions, feelings, success or failure.

1. I tried to find out what Tom's plans are for the summer, but he's giving nothing away. I wonder what he's up to?
2. Alex is a great poker player. He has a face that gives nothing away.

1. Mary gave nothing away when her students asked her what would be on the exam. She said that they would have to wait and see.
2. We asked the manager whether the job cuts were likely to affect our department, but she would give nothing away.