He hopes to extract a promise that troops will take their artillery and tanks out of range of all urban areas.

She extracted a promise that he would visit her and his father regularly.

So extract some promises to improve what you've got.

As per her plan, she defeated him and spared his life after extracting a promise that he would accept a different challenge from her.

Using his father's society and business contacts, he approaches the state governor and extracts a promise that the college may be reprieved if enrollments improve.