Out-stayed means to stay longer than was intended or welcomed, to the point where it becomes an annoyance. The antonyms for out-stayed would be words that convey the opposite meaning, such as vacate, exit, depart, or leave. These words imply that someone is leaving a place or situation willingly and at the appropriate time. Other antonyms for out-stayed could be punctual, timely, prompt, or considerate, suggesting that someone is respecting other people's time and preferences. In short, the antonyms for out-stayed revolve around the idea of leaving a place or situation promptly and courteously.