This spider is quite common but a real pain to photograph because they move so fast which is why I am hopeful that someone can help me improve the exposure of the dark bit with destroying the white bit.
For me it’s hard to brighten the shadows AND not making it look completely shitty. This is as far as I would go. Let’s wait for some other contributions.
I get the impression there’s an out of focus object causing the dark area, not just a shadow:
color is different (greenish), and the spider is unsharp in the darker area.