How do display gallery embedded to the custom post type

I think one good possibility is to add a endpoint to permalink for galleries and then check the template to include in the template_include filter:

add_action('init', function() {
    add_rewrite_endpoint( 'gallery', EP_PERMALINK );
});
add_filter( 'template_include', function($template) {
    if ( get_query_var( 'gallery' ) ) {
        return get_stylesheet_directory() . '/single-event-gallery.php';
    }
    return $template;
});

Now, create the file single-event-gallery.php and put it in your theme folder. You can copy the content of single-event.php and replace the_content() with:

if ( get_post_gallery() ) {
     echo get_post_gallery();
} else {
     echo "No gallery found";
}

You must use URLs like mysite.com/event/a-event-post/gallery/1 (“1” is a random value, any value after “gallery/1” is valid).

I tink it is a simple, fast and easy solution but with these problems:

• It adds the endpoint rewrite rules to all permalinks
• It needs some value after gallery in the URL

To avoid that problems we can define a custom rewrite rule only for “event” post type and define a custom query var to use in the template_include fiter.

add_action( 'init', 'cyb_event_gallery_rewrite_rule' );
function cyb_event_gallery_rewrite_rule() {
    add_rewrite_rule( '^event/([^/]+)/gallery/?$', 'index.php?event=$matches[1]&gallery=yes', 'top' );
}

add_filter( 'query_vars', 'cyb_register_gallery_query_var' );
function cyb_register_gallery_query_var( $vars ) {
    $vars[] = 'gallery';
    return $vars;
}

add_filter( 'template_include', function($template) {
    if ( get_query_var( 'gallery' ) ) {
        return get_stylesheet_directory() . '/single-event-gallery.php';
    }
    return $template;
});

Now you can use URL like mysite.com/event/a-event-post/gallery/. You can generate the URL inside the loop of parent post with (or similar, depends on your permalink settings):

$gallery_url = get_permalink() . 'gallery/';

Note: after you apply this code you need to flush the rewrite rules of your site. You can do that visiting the permalinks settings page and clicking in “save”.