Core Rules wrote:
Players immediately advance to the next stage of a quest as soon as they place a number of progress tokens equal to or greater than the number of quest points the current quest card has.
Quest cards are immediately replaced as soon as players place enough progress on them, and this replacement does not interrupt the current round sequence.
There is always an active quest. So in your scenario, Legolas would be able to use his ability to place progress tokens on the active quest.
Edit: Oops! Responded w/o taking the subject into account. See below for the correct answer.