Board Thread:Skyrim/@comment-11618741-20150726035340/@comment-11618741-20150727002248

From UESP:

If this quest is obtained during the main questline and is not completed prior to finishing the main quest, it will disappear from your active quests. However, you may still kill Paarthurnax at any time after this point; the quest will now reappear in your journal and can be completed normally.

So it might disappear, but it will still be active. The only way I see to get rid of it is to complete it.