Exclude post category in a blog page

In your functions.php file, use pre_get_posts and swap out the -1 in the following code with the category I.D you want to exclude from your posts page.

function exclude_category( $query ) {
    if ( $query->is_home() && $query->is_main_query() ) {
        $query->set( 'cat', '-1' );
    }
}
add_action( 'pre_get_posts', 'exclude_category' );