Do you mean stair hand rail?

Yes

Video link didn't work for me. Can you try again?

Added Youtube link as well.

"Added Youtube link as well."

Where?

It's on the post. Repost here: https://www.youtube.com/shorts/tVg2dNFzTOQ

I viewed your latest video, but can't see what is loose. Is it where the top end of the handrail butts into the wall?

Maybe this? Rosettes

The end that attaches to the wall is no longer tight. If you turn up the volume, you can hear the sound of it bumping inside when I tried to shake it.

The simplest way to deal with that is to drill a horizontal hole through the top end of the railing and install a screw that is long enough to go through the wood railing, through the sheetrock, and into the wood framing in the wall at least 1". You should use a trim head screw -- a special screw with a small head -- and install it with an impact driver. When you're done, the head of the screw should be just beneath the wood surface of the railing so you can patch the small hole with wood filler. If you don't have the experience, skills, and tools to do this properly, get a knowledgeable friend or handyman to do it. It's not hard if you know what you are doing, but easy to mess up if you don't.

I had one that had loosened. My genius handyman angled a screw and drove it in. It’s been tight for a least a year. Pardon my unprofessional description.

Anna-

No need for a pardon. You just described what I was trying to explain, only more efficiently. 😉.

Thanks kudzu9 and Anne for the replies! I wonder if there is a solution without drilling? I wonder how the hand rail is attached to the wall and if there is a way to somehow tighten it?

However it's attached to the wall -- if it's attached -- there is no easy way to tighten it. Use a trim head screw, set the head a little below the surface, and patch the tiny hole. No one will notice.