Past / previous posts password

Hi there, my theme is Maifest, and at the bottom, you can click (past, previous, next post etc). There are 30 or so posts per page, but you can click through to see the next 30, and so on for about 6 pages.

I am wondering if there is a way, that my most recent 30posts on the first page do show up, but, when you click the previous post link, it to be passworded (I hope this makes sense, I am not tech savvy) so the viewer can see the first 30, but cannot see the posts before that without a password.
x