Head inside Tel Mithryn Apothecary and listen out for Elynea Mothren shouting about how unreasonable Neloth is.She'll tell you that she needs some Taproots and these can either be bought from an Alchemist or can be picked up from the corpse of a Spriggan .
Giant Nirnroot Island is an unmarked location located on the northeastern-most island Solstheim, directly north of Frossel . It's a small rocky isle with six giant Nirnroot plants.
The island is inhabited by three leveled Spriggans who appear to have killed a Dunmer alchemist whose body can be found nearby. The alchemist's boat is also at the shore with some minor loot.
Once they have been obtained, proceed to the Headwaters of Harstrad . Another Spriggan lives in this small cave, but once it has been killed activate the headwaters to soak the taproot. Once this has been done, return to Elynea. She will keep two of the Soaked Taproot and request that the other be planted in the withered interior wall of Tel Mithryn .
Travel up the tower and plant the Taproot into the large dark bulge on the wall. Return back to Elynea, who replies "Good. Now maybe Neloth will get off my back about it." and grants a reward