A worker in the greenhouses of Ember, Clary is "tall and solid, with big hands and knobby knuckles. She had a square jaw and square shoulders, and brown hair cut in a short, squarish way." (4.38)
Because Lina's father used to work in the greenhouses, Lina got to know Clary pretty well. She likes how Clary has always treated her as an equal: "Even when she was little, Clary did not treat her like a baby but gave her jobs to do—pulling up carrots, picking bugs off cabbages" (4.38). Clary was also friendly to Lina when her parents died, letting Lina come visit her to talk or just hang out in silence.
When Lina asks Clary whether she thinks Ember is the only light in a dark world, Clary begins to open up, and ponder where life comes from. This is pretty neat for Lina to witness, as she "could see that words were welling up in Clary now; her eyes were bright, her cheeks were rosy" (4.91). It turns out that Clary is a philosophical lady, believing that life is difficult to understand, but also that life has to come from somewhere. That means there must be answers outside of Ember, if anyone's brave enough to seek them. It's that revelation that provides the spark that drives Lina and Doon to explore the path to escape.
Further, Clary has a lot of insight to offer when Lina comes to talk to her about the mysterious message and the mayor's greedy nature. Clary knows enough to suggest "Egress" as one of the missing words in the message's title. This is a major breakthrough—it means the instructions are for how to exit Ember.
Clary is also optimistic, which helps encourage Lina to finish the investigation she started. When Lina complains that deciphering the message seems hopeless, Clary responds, "Don't say that. This torn-up piece of paper is the most hopeful thing I've ever seen" (13.28). If we could have someone who was a combination a friend, a cheerleader, and a counselor, we'd want Clary on our side.
Lina trusts Clary, which is why Lina was going to leave her a message explaining how to get out of Ember. Unfortunately, Lina got captured by the guards and forgot, so Clary is as in the dark as the rest of the citizens about how to escape the dying city. Still, we think Clary's smart enough to remember the general conversation she had with Lina about the instructions on how to exit Ember. But who knows what the atmosphere in the city will be like after the kids depart?