How can I obtain the New Moon Priest Style?
You can obtain the New Moon Priest Motif chapters in the Dragonguard Supply Chest.
To unlock the Dragonguard Supply Chest you need to earn the Dragonguard Operative achievement.
To earn that achievement you need to complete 30 Quests related to the Dragonguard.
That can be Main story quests of the Dragonhold dlc as well as daily repeatable quests from Chizbari the Chipper and Dirge Truptor in the Dragonguard Sanctum.
The Dragonguard Supply Chest will appear infront of Dirge Truptor in the Dragonguard Sanctum.
You can open the Dragonguard Supply Chest once per day.
Complete the first two main story quests "the Dragon's Lair" and "Reformation" of the Dragonhold DLC to unlock the Dragonguard Sanctum.
Where can I find the Daily repeatable quest givers in the Dragonhold DLC (Southern Elsweyr)?
Is it part of the ESO Base game or do I need a DLC or ESO plus subscription?
To be able to obtain the New Moon Priest Style you need to own the Dragholhold DLC or have an active ESO plus subscription.
What do I need to craft the New Moon Priest Style?
To craft the New Moon Priest Style you need the style material Aeonstone Shard which can be found in the Dragonguard Supply Chest in the Dragonguard Sanctum
Can I see how the New Moon Priest Style looks like?
Sure you can! I have created a youtube video for this topic:
Monday, the 24th of February, 2020
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ESO Jephrine Paladin Style
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ESO Dragonguard Style - Showcase of the Dragonguard Motif in The Elder Scrolls Online