Once you and Viarmo are done reconstructing (or lying about) the rest of the Verses of King Olaf, he tells you that he needs to go present this to the Jarl in her court immediately. He tells you to come along with him to court, and then ends the conversation, heading for the door of the college.
Whether you accompany him or not, Viarmo will go to the Blue Palace and have a seat on a bench in the front hall. There, he waits for you to talk to him- once you do, you can ask him if he is ready. He says his voice is, and he hopes the verse is as well. The old mer will then rise and head up to the second floor of the Palace, where Jarl Elisif holds court.
On reading the (heavily modified) verse to the Jarl, he gains her approval both for the verse and for the Burning of King Olaf, reinstating the pending festival. She is particularly happy to do so if you’ve gone overboard in your ‘recreation’ of the missing portions, as befits her nature displayed thus far as a Jarl prone to melodramatics and overly grand gesture.
The Jarl even grants a reward to the college for locating (making up) the poetry, and then dismisses Viarmo from the court so that he can make ready. The elf turns to you and thanks you for your help, telling you that this is a great achievement for the College. He also instructs you to go find Jorn, the man who was preparing the wicker effigy for the burning, and inform him that his preparations should be finished soon, as the festival is actually going to happen.
You may ask Viarmo about your admission to the College as a full-fledged bard, and he will let you know to have a little patience (which is the same answer you get if inquiring about any form of reward for your work): you will gain the benefits of your quest in the evening, at the Burning of King Olaf.
Return to the Bards’ College to find Jorn, who will likely be lurking about in the main room on the first floor. He greets you eagerly, and is happy to hear his preparations won’t go to waste. The celebration, he says, will be held in the evening, so come back after it’s dark- this actually means sometime around eight PM or so, regardless when ‘evening’ is that particular day.