Surrender, as in They gave themselves up to the police. [Second half of 1500s]
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.
How to use give oneself up in a sentence
It is hard entirely to share another people's life, to give oneself up to it, to be received into it.A Poor Man's House | Stephen Sydney Reynolds
For it is not enough to give oneself up to the sacred duty of succour.The New Book Of Martyrs | Georges Duhamel
It was impossible to be with her and not give oneself up to her charm.The Second Violin | Grace S. Richmond