is it possible to install new WordPress in an old WordPress folder?

Yes it is possible, one simple way is to delete wp-config.php and add wp-config-sample.php then open the site in the browser, it ask you to install the wordpress. So, install a fresh wordpress.

After that open your phpmyadmin, select the database which wordpress created for you, then check all tables of this database then select DROP, and confirm the action.

Now you have a wordpress site without database, after this go to import tab and select your old database, it took some time to revive your old db depending on the db size.