As @damium@programming.dev says you may be able to do this with find command. This command lists all PDF files under ~/tmp that were created more than 7 days ago and does a directory listing. You could use this as a basis to move create an archive of individual files.

find ~/tmp -ctime +7 -iname “*pdf” -exec ls -rlht {} \;

The find command also has a -delete flag.

I have in the past used this combination to implement file management. I don’t have access to the script any more. I don’t remember why we used a shell script rather than logrotate as per @oddityoverseer@lemmy.world