The phrase "sate around" typically implies a state of satisfaction or lack of activity. Therefore, antonyms for this phrase might include expressions that connote a sense of restlessness, contentment, or action. Some opposite phrases could be "stay active," "remain unsatisfied," "pursue ambition," or "do not linger." These opposing phrases suggest a feeling of drive or the urging to accomplish more. Be sure to choose the opposite that best suits the context in which the original phrase is used to add appropriate meaning and context.