I basically need to remove a subdirectory from a path:

For example:
https://my_website/images/phocagallery/000_new_site/rest/of/the/path/
should become:
https://my_website/images/phocagallery/rest/of/the/path/

I tried (among other things...)
From
^/images/phocagallery/000_new_site$
To
{siteurl}/images/phocagallery

But no redirection is taking place. What am I missing? (I did clear my browser's cache)

Other redirections not involving regex work just fine, for example simply changing an old picture name by the new one (so long as there are no change in directory structure).

What I want to do is first a rule to change the directory structure, and then a rule to change the file name (not all files changed).

So far the picture' name is redirected correctly when there are no directory changes. Now I need to figure out how to correct directory structure.

Thanks for your guidance.

Works perfectly.
Thank you very much for taking the time to give this specific answer, it helps me understand better the macros used in it.