Can you grout tile over the existing grout for a fresher look?

no, you can however paint grout

You can purchase a product called Grout Renew. It comes in many colors, so you can even change the color of your grout if you want to. One bottle covers approximately 100 square feet. You can get it at Floor and Decor, Home Depot or amazon. I have changed the color of 2 bathrooms several years ago and they still look brand new. Make sure you clean your floor first. It is a tedious project for a large area, but you can do it in several days.

You can regrout. In the tile section of a home improvement store, there's a small hand tool called a grout remover. It goes down into the grout lines and cuts it away. Then simply regrout your tile.

No, you cannot grout over old grout. I wish you could, mine need it! As Dee posted, you could use a product designed to go over grout - still quite a bit of work involved.

If the grout itself is in good shape, consider a grout stain: https://www.wikihow.com/Change-the-Color-of-Grout

No old grout needs to be removed. If it in good condition you can clean it, paint it, seal it.