To see an extra quest icon next to your other quests, you need to turn on Quest Tracking.

Here's how:

๐Ÿ‘๏ธโ€๐Ÿ—จ๏ธ Talk to the character who gave you the quest. In the quest description window, find a round icon with an eye in the upper right corner. Click it to turn on Quest Tracking.

๐Ÿ‘๏ธโ€๐Ÿ—จ๏ธ Or, open the quest book and find the quest you want to track. Next to the quest name, there's a round icon with an eye. Click it to turn on Quest Tracking.

๐Ÿ“‹ You can turn tracking on or off for any quest. Track the quests you want quick access to.

๐Ÿ“‹ You can track up to four quests at a time.