slake
To fully satisfy a strong need, usually thirst or desire.
To slake means to satisfy a thirst or strong desire, especially by giving it what it needs. When you come inside on a hot summer day and drink a tall glass of cold water, you slake your thirst. The word captures that feeling of relief when something you've been craving is finally satisfied.
You'll most often see slake paired with thirst, but it can apply to other strong wants too. A curious student might slake her desire for knowledge by reading everything she can find about ancient Egypt. An explorer slakes his longing for adventure by traveling to remote places.
The word suggests complete fulfillment of an intense need, like pouring water on a fire until it goes out. You wouldn't say you slaked your mild interest in a topic. You'd say you slaked your burning curiosity about it.