Changing menu order of a specific plugin in dashboard

I could see “WP Links Page” is a custom post type, so if it’s not registered by your own code, e.g. it’s registered by a plugin (using register_post_type()), then you can use the register_post_type_args filter to change the menu_position argument like so:

add_filter( 'register_post_type_args', 'my_override_register_post_type_args', 10, 2 );
function my_override_register_post_type_args( $args, $post_type ) {
    // Move "WP Links Page" to below the "Pages". You could also try using 21 instead.
    if ( 'wplp_link' === $post_type ) {
        $args['menu_position'] = 20;
    }

    return $args;
}