The following chapter provides a detailed description of the gameplay during The Looming Shadow. You will find tips that can help you complete the quest in the most effective way possible.
The quest will appear in your journal right after you complete The Mountain that Fell. Your task will be to get to the Meridian, and discuss the plan of defending yourself against your enemy.
In the Meridian, head to the Palace, and talk to Avad. After a longer dialogue, you will be sent to Marad. Talk to him to continue your quest. During the conversation, you will learn about his defensive strategy. He will inform you that you can rest before the final battle in Olin's apartment.
Resting equals completing your task and proceeding to the final mission, so don't do it until you stock yourself with enough resources, ammo, med pouch and best armor available.
Instead, head towards two spots marked by your indicators. These are abutments where you and your allies will defend yourself against hostile machines. Take your time to study the area carefully and talk to people, whom you met during side and main quests.
Use Focus to find them all. Once all is done, head to Olin's house and rest before the final battle. You will complete your quest and Horizon Zero Dawn epilogue will begin. During the cut scene a new quest will begin - The Face of Extinction.