Hi @CritterCrew please allow me to give you a warm welcome to the Ubisoft Forums! I'm glad to help you, and I can empathize with your annoyance of the "New Quest" alert never disappearing! This issue was previously report, but confirmed as fixed in a previous patch. However, if you're having it currently on the 1.6.0 title update, we can look into investigating this again. To continue, please try verifying the game files in Ubisoft Connect to see if there's any improvement.
Should the problem continue, please capture a video of you go...