WordPress comments settings are managed from your admin area dashboard Settings -> Discussions page. There are options that allows you to automatically close comments after a give number of days, you can completely turn off comments or make comment form available only for logged in users etc.
When a post with closed comments shows up on the frontend of your website, it automatically displays ‘Comments are closed’ notification to your website visitors. In this lesson you will learn how to hide this notification.
Default WordPress installation doesn’t provides you option to remove this notification but by using Remove “Comments are closed” plugin you can do so very easily.
Start by installing Remove “Comments are closed” plugin in WordPress
Once the plugin is activated, it removes “Comments are closed” text from your posts, automatically. No configuration options to set.