Graphics editors like YY-CHR and Tile Layer Pro don't edit the in-game palettes for you. The only benefit of changing them within the editor is to make the graphics more visually friendly for modifying them. If you want to modify the actual in-game palettes, you have to use a hex editor and/or a special emulator that includes a hex editor to find the correct ROM offsets and modify them that way. The only other way would be if a game-specific utility is programmed to allow you to modify the palettes with it.
From your previous posts, you mentioned that you're working on a Super Mario Kart hack. The Super Mario Kart ROM map
has a few palette-related offsets.
GlitchCog documented the palettes, if you search for their site, although it reportedly doesn't always work. Maybe the information could be documented elsewhere. I would like to believe that Stifu would include documentation with the main notes, but since I don't hack this game, I haven't bothered to look, so you can try checking it on your own.
From a quick Google search, apparently Epic Edit, the Super Mario Kart editor, features a color palette editor tool.
In any case, you can try to seek out any and all documentation that already exists first to study from, and maybe see if there are tutorials covering the specific details for what you hope to achieve. Again, since I don't hack Super Mario Kart or SNES games in general, I can't be more specific than that.
If you're not still referring to SNES like you were previously, and you're actually looking into modifying palettes in NES games like the original topic creator, then perhaps I can provide you with more specific details in assisting you. However, one tip is to be as specific as possible with your posts and requests for help. You don't want for the people you're asking for help to have to assume any details in trying to figure out your problem, or else it's less likely that anyone will want to bother. If it's not the same game as before, then which game(s) are you hacking?
Best of luck.