Display css ONLY on most recent post of specific category?

From the context of your question I understand that you don’t use next_post_link and previous_post_link for the implementation of the Next and Prev buttons, so you have to use CSS to hide them appropriately.

next_post_link and previous_post_link simply don’t display the links if the current post is the last/first on the loop, so I think it would be better to add them in your template instead of using CSS.

You can check the documentation here: