There are many occasions when a student is rejected, takes a gap year, and successfully gains admission to a college after that.
Are you asking about being rejected by Harvard for example, then reapplying to Harvard and being accepted? That’s extremely unlikely and I haven’t heard of that. There’s quite a famous story here on CC of a student who applied to mostly top schools and was rejected at all. He took a gap year, applied to MIT, among others, and attended MIT. He applied to Princeton and was rejected again, if I recall.
He did a lot of meaningful activities in his gap year and approached his list with a new outlook, primarily in that he was very thoughtful about where he applied. It worked for him. The best option is to ensure you have a realistic list of schools to apply to. It’s great to aim high, but understand that those schools only have room for a tiny fraction of students who apply. If the goal is to attend college, you can succeed at more than just the top 20, or even the top 100. Good luck.