What you are proposing is possible, but not recommended.
Chances are high that the old shower wasn't waterproofed any higher than the pan. The new tile isn't going to address that issue. The new tile will only be as good as the old tile. The only change will be cosmetic. Then there will be an issue of what to do where the tile edges stop and the old tile is exposed.
As much as we could use them, there are no tile police. If you really want to do this;
1- Clean the walls like they've never been cleaned before.
2- If the tiles are glossy, scuffing with a diamond abrasive disc will help the thinset grab much better.
3- Use a dry powdered thinset (the type in a bag you mix with water) specifically labeled for use over tile. Do not use anything from a bucket.
3B- leave a gap (not grouted) around the perimeter of 1/8" to 1/4" to allow for expansion at all changes of plane (wall to floor, wall to wall).
4- Caulk the perimeter joints at the changes of plane (wall to floor, wall to wall) using 100% silicone. Not latex or siliconized latex.
6- Wait 3 or 4 days then seal with a quality sealant like miracle 511 or Aqua mix.