This is not a traditional quest, but represents an overarching mission the player has.
At the end of the quest The Stars Have Eyes, Harper will give the player a lead for another Watchtower base in the Kumasi system.
After the player tracks this lead, finds and destroys the corresponding Array, and then returns to Harper - she'll mention Dr. Laine has set up a clinic. Then, when the player goes to leave the conversation, she'll tell them to wait and will describe the Watchtower Arrays. She'll then tell the player they can read more on her terminal.
Reading the entry will provide some more in-game explanation and then start a new quest called "Watchtower Arrays", which will list the first Major Array and its linked Minor Arrays.
This is an optional tracker that can be toggled via that same terminal entry (ie. selecting the entry again will hide the quest objectives; then clicking again will re-display them).
From here, the player is free to do things in the order they like, with the ultimate goal of destroying the five Major Arrays.
There are two requirements to start another branch of story narrative.
As the player engages in Watchtower's mechanics, they raise their profile with the Watchtower faction to a numeric level of 10,000 - which is tracked silently under the hood.
The easiest way to do this is to destroy the 5 Major Arrays. Alternatively, the player can engage in a variety of other things to advance this:
Once the player knows about Starborn and have advanced their profile with Watchtower, a mini-quest starts to kick off the next event.