*spoiler*
If you mean *the* contract between the leads: From what I could tell, it was an oral contract, not written, as it was really only an agreement based on on a threat.
It went basically "Pretend to be a playboy and a jerk while I control everything behind the scenes or I hurt your mom. Oh and she'll die if I die, so you and no one else can kill me". Now she's like "I don't want anything, but I don't wanna die either, so keep me alive or your mom will die when I do".
I think the original 'evil' duchess had some huge final goal/purpose (some huge dark family secret that no one knows about yet), and promised to give the mom back after that goal was reached. Since he had the mom back, he could easily invent a bull reason to kill the duchess later on. The kicker? I think the original evil duchess didn't care if she died, because the whole goal was to destroy the empire from the inside... so she was just holding on to the mom hostage as she quietly set up the empire's tragedy, gave the mom back, then didn't care if she died later (because she knew the empire was now doomed).
The emperor thought she was simply greedy and cruel, but I suspect her actions were to literally sneakily set up the entire plot of the empire falling. I think she likely worked with the empress dowager in the original plot. The original duchess used the emperor's love for his mother to keep him powerless as the duchess ruined everything, and had he known what she was doing, he would've had to choose to give up his mother's life for the sake of the empire. Maybe that's even why he killed his self in front of his mom in the original- he realized by giving in to the duchess and saving his mom, he had allowed all of those terrible things (like the slave trade) to rot his empire from the inside.
The big question is WHAT HAPPENED TO THE DUCHESS? What big secret made her go from loving the prince to dedicating her life to destroying everything??
Sorry, my brain went for a ride, have a good day!
What is the contract about like what does it say on it