gain on (someone or something)
To begin to make up the difference between oneself and someone or something, so as to be at an equal level, status, or point of progress. If we speed up, we might be able to gain on the car ahead of us!
gain on someone or something
to begin to catch up or move ahead of someone or something. We were gaining on them when they suddenly sped up. Our horse was gaining on the horse in front.
gain on
v. To get closer to something or someone, often in pursuit; close a gap: Run faster—the stampeding cattle are gaining on us!