The saturation of red is reduced. The reduction can be done with Photoshop's Hue & Saturation adjustment because it can be adjusted to affect more to red than other colors. If you test it, you will notice that it causes an harmuful artefact on the face, but that's fixed by inserting hair.
That can in theory be a random incident, the hair supplement can have been inserted for other reasons. I suspect both images are different versions of a third version which should be considered to be the original.
But let's stay with your problem "how the left version can be converted to the right version". For it the hair must be repainted. There's not enough details in the left version which could be adjusted to the well visible hair details in the right.
In the right there's some light outlines added. They can be drawn or they can be made with a filter it the work has been a multilayer image. I guess they are drawn.
With dodge brush one can quite easily add some gloss to the clothes, the knife and the horseshoe. Burn brush can have been used to give little darkening to the back tie and the wrinkles of the cloth. The white piece in the bottom skirt edge is repainted off.
Conclusion: It's not an effect, one must be able to paint something, too if he must start from the left version and get the version in the right.