The phrase "leave the dust" can be interpreted in a few different ways, so let's explore some antonyms for each possible meaning.
If "leave the dust" refers to abandoning a project or goal, the antonyms could include finishing, completing, achieving, or succeeding. These words suggest that instead of giving up, you should persevere until you reach your desired outcome.
If "leave the dust" means neglecting or forgetting something important, antonyms could be attend to, take care of, prioritize, or remember. These antonyms emphasize the need to pay attention to important tasks and responsibilities.
Finally, if "leave the dust" is taken literally as in leaving behind dirt or debris, antonyms might be clean up, buff, polish, or shine.