An example of the use of with that as a conjunction is in the sentence, "She lost her patient, and with that, she quit the project," which means that as a result of losing her patience, she quit the project.
With That Sentence Examples
They signed on with that ranch in Wyoming.
Only Quinn seemed pleased with that result but when we tried to question him about it he refused to discuss the matter.
There's nothing wrong with that girl!
Don't leave me here alone with that mad man on the loose!
He was later arrested on another rape, charged with that crime, and sent away.