"Gat around" means to move or travel from one place to another in a leisurely or aimless way. Its antonyms would be "stay put," "remain stationary," or "settle down." These words refer to the opposite of wandering around without a specific destination. To stay put would mean to be in one place for an extended period, while to settle down would imply finding a permanent location to stay in. Using the antonyms of "gat around" in a sentence might look like, "Instead of gatting around, why don't you stay put and relax for a while?" or "It's time for you to settle down and find a stable routine.