Hello Michael, 

I guess it will not be a problem if you already have it done. Can you show me somewhere how this tab look and what actually do? 

I'm not sure what I'm looking at this screenshot? This is Add Event Tab?

Who made this Author Tab for you? Can you ask him to show it for me somewhere? 

Here's permanent solution:

1) Open file stachethemes_event_calendar\admin\view\events\addedit.php

Edit line 45 from:

        <?php do_action('stec_admin_addedit_event_tab'); ?>

to:

        <?php do_action('stec_admin_addedit_event_tab', $event); ?>

This change will be included in the next update.

2) In your theme functions.php file add following php code:

add_action('stec_admin_addedit_event_tab', function($event) {
    if (class_exists('Stachethemes\Stec\stachethemes_ec_main')) {
        if ($event && $event->get_approved() != "0") {
            ?><li data-tab="author"><?php _e('Author Info', 'stec'); ?></li><?php
        }
    }
});
add_action('stec_admin_addedit_event_tab_content', function($event) {
    if (class_exists('Stachethemes\Stec\stachethemes_ec_main')) {
        $stec = Stachethemes\Stec\stachethemes_ec_main::get_instance();
        $path = $stec->get_path('ADMIN_VIEW') . '/events/';
        if ($event && $event->get_approved() != "0") {
            include($path . 'tabs/author.php');
        }
    }
});

This way the author tab will be visible at all times.