An Unexpected Engagement
This quest will be available after completing "Heraldry from a Herald" if you've continued to pursue a romance with Josephine. If you do not want to pursue a romance with her you will have the option to turn her down during this quest line.
Josephine will inform you that she has been engaged to marry without her knowledge by her noble family and in order to defend her honor you will have to duel the man she is betrothed to. Before the duel you will need to complete at least one war table operation. After that you'll meet a representative of the suitor's in the courtyard at Skyhold and then travel to Orlais to begin the duel.
The overall outcome of the quest depend on whether you choose to continue pursing a romance with Josephine or not.
GAMER TIP: If you have the Arcane Knowledge Inquisition Perk unlocked you'll have unique dialog options that allow you to run a bonus War Table operation to dig up dirt on Josephine's suitor. This will allow you to confront him with the information during the duel and gain the upper hand.