There are many Tash love quests and events in "Dragon Age: Shadowkeep" in the game, and Tash's love quest event is firstly the dragon hunter, which can recruit Tash, and then the dragon course. (Dialogue), Tash teaches you about dragons and their relationship with the Lord of Wealth.
How to do the love mission event of Tash, the Shadow Barrier Guardian in Dragon Age
The Dragon Course will expire if not completed before the Siege of Westhope, but it is not a requirement for a romantic relationship with Tash, although it does provide greater insight into Tash's personality and increases favorability.