This quest is available after completing The Bloodstone Chalice. Talk to Garan Marethi or some other Vampire in Castle Volkihar. They tell you to speak with Feran Sadri for an assignment. Locate Feran Sadri in the castle and ask what you can do to help. Feran has been performing a little research on the Blood Chalice. He believes we can prolong its salutary effects if we infuse it with potent vampiric blood. He has located the petrified remains of an elder vampire. Bring them to him, and he should be able to extend the effects granted by the blood chalice.

This starts the quest:

Ancient Power
Feran Sadri has sent me to retrieve the Ancient Vampire Ribcage from Uttering Hills Camp. After infusing the magical essence lingering in the remains into the Bloodstone Chalice, the power granted to use from drinking it will last longer.

Retrieve the Ancient Vampire Ribcage from Uttering Hills Camp.

You can repeat this quest for a total of seven times. Each time you will need to get a different body part. These include:
Ancient Vampire Head
Ancient Vampire Arm x2
Ancient Vampire Leg x2
Ancient Vampire Hands
Ancient Vampire Ribcage

Location will be random for each body part. For example, instead of Uttering Hills Camp, you could get sent to Druadach Redoubt, Shimmermist Cave, or Orotheim.

The Uttering Hills Cave is west of Windhelm, but as mentioned the dungeon assigned to you could be a different one. Other than that, the quest is identical. Enter the dungeon and fight any enemies there, you will most likely find the Ancient Vampire body part in a chest towards the end of the dungeon.

Return to Feran Sadri at castle Volkihar when you are done. You receive some potions of blood as a reward.

This completes the quest, Ancient Power.