Now that you’ve retrieved the blade you needed, head back to Whiterun to talk to Danica Pure-Spring again.
The priestess is honestly (but gladly) surprised to see that you not only survived, but returned with the needed blade. However, from her perspective the blade is something foul, created for its ability to harm nature, including the Eldergleam. Therefore, she also asks that you take the blade to the East, to the sanctuary of the Eldergleam, and use it yourself to collect the needed sap.
Moments after you agree, you’re approached by Maurice Jondelle.
Maurice explains to you that he is a pilgrim- a follower of Kynareth who wanders in search of the divinity’s holy sites. He has wanted to visit the Eldergleam for some time, but Skyrim’s not very safe for a lone, unarmed traveler, so he’d like to go with you. Allowing him to travel with you will let you take an alternative action once you’re at the tree itself, giving you a second way to complete your quest. If you don’t feel up to having an unarmored man travel with you, though, feel free to tell him where to shove it.
The Eldergleam Sanctuary is located in the Eastern half of Skyrim, thoroughly out in the middle of nowhere. Getting there thus becomes a bit of an adventure in its own right- even the fast travel points somewhat near to it are often a good distance off, and you’ve got even more walking to do if you haven’t gone meandering randomly about the East of Skyrim previously.
From Whiterun, the directions are as follows:
Head to the main road South of Whiterun, and follow it going East, past the Honningbrew Meadery. Use the stone bridge to cross the river (keeping a watch out for wolves) and then follow the cobbled path as it goes around the Throat of the World to the North, alongside the river that winds around the base of the mountain as well. Keep an eye out for roadside encounters- you will quickly come across either a group of bandits posing as some Imperial soldiers they murdered, or a lone Orsimer bandit, along the road. Other bandits are in their usual locations, including the pair of towers over the river (particularly if it’s been a while since you last cleared the place out).