“Elmus Favor Quest” is a Miscellaneous quest in Skyrim - Dragonborn
While Thirsk Mead Hall is held by the Rieklings, this misc quest is available provided you have not killed the Nords.
Visit Bujold's Retreat and talk with Elmus. He will ask you to head into Thirsk Mead Hall and retrieve him a bottle of Ashfire Mead. Head into the Mead Hall (being shown in if this is your first visit).
Any bottle of Ashfire Mead will work for this quest. It does not need to be taken from Thirsk Mead Hall.
Talk with Elmus inside the Mead Hall. He will ask you to collect more Juniper Berries. While he does tell you that these berries cannot be found on on Solstheim, but there is one plant outside Nchardak.
The Juniper Berries can be found all over Skyrim itself. The most berries can be found within the the Reach. Collect the required number, pull them from your supply or buy them from Apothecary Merchants. Return to Elmus after that to collect your reward.