Tag after is a phrasal verb that means to follow or pursue someone closely. The antonyms of this phrasal verb would be to lead or guide someone, to go ahead of them, or to take the lead. Some possible antonyms for tag after include lead, guide, direct, precede, or command. When you lead someone, you are showing them the way and taking the initiative. You are not following them or chasing them. Similarly, when you direct someone, you are pointing them in the right direction and instructing them on what to do. By contrast, to tag after is to trail behind someone and mimic their movements.