Jarl Balgruf isn't seated at his throne when they enter, though he moves to it when Glint indicates she wishes to speak with him - his housecarl does indeed seem pretty protective of him, instructing the two women to stand at a certain distance (only allowing them even that close due to the Jarl overriding her paranoia).

He's an old man. Calm, and prone to stopping to ask his circle of advisors questions - though he freely overrides them as well - and he listens seriously to Glint despite one advisor pointing out the clear ties to Sheogorath. ("The laws of Whiterun do not permit guilt by association," is the Jarl's response. "She will be judged on her own actions.") 

And, after a discussion - he stands and gestures for them to follow him. "I hadn't thought it would become relevant... But my court wizard has been looking into dragons of late. He'll have something for you, I believe."

"A fortuitous coincidence, Jarl Balgruf." And following him to the wizard.

Who's talking to an odd woman, a dark grey cloak covering her form with the hood pulled far over her face - both fall silent as the Jarl and his guests enter. The wizard starts rambling about expeditions immediately, but she seems to just be watching - 

Especially Elerki.

Yeah, she gets it. She doesn't have any god-marks. No, not even hiding under her hair. Yeah. No need to fuckin' stare.

Whatever.

She steps over while Glint and the wizard discuss some old records he wants fetched from an ancient barrow - one without any living family to intercede, and one he's had trouble getting a priest of Arkay to help with, apparently.

"You're the one who saw the dragon first, right?" she asks, voice soft and low. 

"The one who survived, anyway."

"No one else did?"

"Not that I noticed. I saw a lot of people die."

"And Helgen was no tiny encampment... I haven't seen a dragon in action. You have. I'd like to sit down with you to go over how it fought." She glances at the wizard, frowning a little, then back to Elerki. 

"But we need a way to kill them, reliably, without holding our breath for a hero out of legend."

"That won't be easy."

"No. It won't."

"But 'lay down and die' isn't an option I'll accept."

"The biggest problem is that it can fly, and fast. You'd need a lot of archers to have a chance of hurting it, and while you're trying to line up your shot, it's breathing fire down at you."

"Might be a question of defensive architecture, though that's slow to change without a lot of alteration mages... Elemental resistance enchantments exist, though, and we might be able to find a cheaper source to outfit archers with, and invest in better quality bows..."

"And you'll need people who are capable of standing firm. Half the soldiers cut and run before the first pass was finished."

"A question of training, as much as anything."

"The legions who stood firm against the Gates of Oblivion weren't any braver at heart than the men of Skyrim today."

"I can't speak to ancient history. But the dragon was loud. You could feel its roar in your bones. Shaking the world."

"It almost felt like a magical fear effect."

Hum. "Not impossible... And harder to defend against, at least affordably and at any kind of scale..." 

"Yeah."

"Did it speak at all?"

"I'm- not sure. Not in any language I know."

"There's - evidence, in the old tombs, that the Ancient Nords used a language they learned from dragons as an upper class or priestly tongue..."

"I wouldn't know."

Hum. "Thank you for talking to me."

"Good luck saving the city, or whatever."

"You won't stick around to help?"