Applying colorpalette to existing images

Chuck's approach is the most viable 1-1 swap out technique/approach of using Color Tables is probably best.

If you knew all your images were coming in had some level of consistency, like are they all various images of red lips that you want to swap to blue lips, you could create a Hue & Saturation adjustment layer with those specific changes to only red values. Then save that value so you can easily load it each time or run it as a batch/action on your folder of images.

You may  fins this site helpful:

Customize indexed color tables in Photoshop

I believe you can do that with index color. Create and save a table then apply it to an image. index color is very limited, so you normally will want to put the image back into another mode so that you can add layers and do other functions with the file.