Dragon Age Inquisition -- In Hushed Whispers

I believe once you completely explore both sides of the dungeon and rescue the companions in prison, you return to that drawbridge and enemies will lower it and attack you. Specifically, I think you have to talk to Fiona before you can move on. Once you talk to her the next quest objective should show up on you map. If you have this and the drawbridge isn't lowering, try reloading before talking to Fiona and activating the new objective again.

Here is the wikia walkthrough, just don't scroll down to far to avoid spoilers:

http://dragonage.wikia.com/wiki/In_Hushed_Whispers

Another walkthrough:

http://ca.ign.com/wikis/dragon-age-inquisition/In_Hushed_Whispers