Word meaning "improves over time"

Solution 1:

Relationships can thaw:

to abandon aloofness, reserve, or hostility

The word carries connotations of something happening over a period of time.

Solution 2:

For me, it would depend on what aspect of the meaning I want to emphasize.

If I want to emphasize the passage of time, I would use the verbs like mature or ripen, e.g., "My fondness for Dorothy had ripened into love."

If I want to emphasize the aspect of improvement, I might use verbs like promote or foster, e.g., "This plan will promote confidence in our ability to deliver."

In the specific context of trust, I'd use earn, e.g., "I spent the entire semester earning her trust."