The Dragonborn tries to enlist the aid of the Jarl Balgruuf the Greater however, the Jarl will say that he cannot try to capture a dragon while Whiterun is under threat of attack. Whoever is picked will say that they must talk to the Jarl of Whiterun to try and convince him to let them use Dragonsreach, which was originally designed to capture and house a dragon.

The Dragonborn must talk to either Paarthurnax, Arngeir, or Esbern. If I can get the Greybeards to host a peace council, I can try to convince the Imperial and the Stormcloaks to agree to a truce in order to defeat Alduin, who is a threat to both sides of the civil war.

The Jarl of Whiterun won't help me capture a dragon as long as the civil war is raging.