give under threat of
give (something) under (the) threat of (something)
To yield something because one has been pressured or coerced to do so. He's one of our best agents—I bet he only gave that classified government information under threat of death. I gave the headmaster the truth about the plagiarism epidemic in our grade under the threat of expulsion.
give something under (the) threat of something
to give something only because one is threatened. He gave the money under threat of exposure. I think that is blackmail. You are asked to give your testimony under the threat of being jailed if you don't.