Is the universe older than 13.7 Billion years? I came to know that the cosmic horizon is the part of universe beyond which we cannot see. So if the light from 13.7 billion years ago is what we can observe, does that mean the universe is older than that and we can't see it?
No, the oldest light we can see is as old as the Universe$^\dagger$. This is simply because light started traveling at that time, so after one year you'd se light that had been traveling for one light-year, after 1 million years you'd see light that had been traveling for a million light-years, and so on. There  is (most likely) more Universe beyond the horizon, but light from those regions just haven't had the time to reach us yet.

You might think that the distance to the cosmic horizon today is 13.7 billion light-years, but because the Universe is expanding, the distance is much larger (in fact 43.6 billion light-years).



$^\dagger$Because the Universe was opaque the first 380,000 years, we can't see all the way, but that's a technical detail.