Where's the new hair?

I checked Gold Saucer, the achievable shop, and even the PvP shop.

I don't see it listed in the patch notes. Might be coming in a couple of weeks as a new Ishgard restoration reward.

Ishgard seems likely, unless it's another hairstyle that gets unlocked at Gold Saucer only after completing a specific quest (like the one from the Ivalice quests).