New main objective: Talk to the heroes of Sovngarde
You can now cross the bridge that Tsun was protecting. Soon enough you should reach Hall of Valor (screen above), so head towards the main entrance gate. Inside the Halls of Valor, listen to a short conversation with Ysgramor, who will tell where to look for heroes of Sovngarde.
The mentioned heroes can be found on the right (screen above) and they are: Hakon, Gormaith Golden-Hilt and Felldir. You don't have to speak with each of them, just listen out to what they have to say. The heroes will afterwards head out to battle Alduin, though you will take care of that issue during another main quest.
Main quest unlocked: Dragonslayer