When in Photoshop:

1. Add a duplication layer
2. Choose the dodge tool and set it to >=50% for the highlights
3. Apply it all across the area that needs increased local contrast
4. Double click on the duplication layer and set the blend mode to “luminosity” with “blend if = gray”
5. For the underlying layer pull the “dark handles” to the right to limit the effect to the lighter parts
6. Then split the “light handles” while pressing “alt” to “feather the effect on the lighter parts.
7. Repeat reversed with the “burn-tool” for adding local contrast with the dark areas
8. Adjust the opacity of the duplication layer for finetuning

Note: Depending on the initial contrast in your picture you might want to also affect the mid-tones with the dodge- or the burn tool

Adapted to Photoshop based on a Video Tutorial for Lightroom shared by Serge Ramelli