You must have returned the relic to the Qunari and saved Isabela to access this quest.
Visit The Hanged Man at night or during the day and converse with her. Regardless of what response you choose, the end result is that Isabela will rejoin your party.
The third conversation option is the only one that offers approval changes.
- "You're still my friend." at a high friendship relation provides Isabela: friendship (+15), but if at high rivalry provides Isabela: friendship (+25)
- "No, you're not." at a high rivalry relation provides Isabela: rivalry (+15), but if at high friendship provides Isabela: rivalry (+25),
Romance and companionship are reinstated.
Isabela is a selectable companion again.
- pcps3xbox360 It is possible that, when addressing Isabela in the beginning of Act 3, she will just say one of her idle banter lines. She is still not available as a party member.
- pc Opening Isabela's debug menu via the console (runscript zz_isa_debug) and selecting "set base" from the first selection, will resolve the issue and allow you to initiate the quest.
- pcps3xbox360 Leave and come back; if this doesn't work, leave and do another companion's quest (not Varric's, as it does not require leaving the area), then return.