It's the very last quest in this year's epilogue quest chain, i.e. the quests you unlock by doing the Greymoor and the Markarth stories. When I left the keep after the celebration, the new quest giver was there.
The UESP wiki indeed lists quest giver Ardanir as becoming available after concluding the Markarth quest line in the quest A Feast of Souls. So it seems you don't need to finish Second Chances.