If you agree to do something on the understanding that something else will be done, you do it because you have been told that the other thing will definitely be done.

双语例句例： Poverty forced her to surrender him to foster families, but only on the understanding that she could eventually regain custody.

贫困迫使她把他交给了寄养家庭，但前提是她确定她最终一定能重新获得抚养权。