After dealing with Duke Abele, you will be tasked with obtaining Delilah's secret.
From the position of where you dealt with the Duke, (either the office or bedroom depending on your approach). Leave the room and you should find a flight of stairs. Go to the very bottom of this staircase and you will find two guards in the pantry.
Deal with them how you see fit and then go to the marker for hidden passageway. To the left of the marker are some shelves, at around eye level, there is a small button, press it and the door will open.
You will see the item in front of you, along with a clockwork soldier patrolling, grab the item while out of sight of the soldier (the soldier will despawn once you have the item).
Enjoy the cut scene and your cheev will pop