Notify admin (by email) if post added with specific tag

Here is some simple code provided straight out of the WordPress codex.
If you are not familiar with the Codex, you should make time to do so.
https://codex.wordpress.org/Plugin_API/Action_Reference/save_post

function my_project_updated_send_email( $post_id ) {

// If this is just a revision, don't send the email.
if ( wp_is_post_revision( $post_id ) )
    return;

// get the post data and check for tags here ...
$newpost = get_post( $post_id );
// Now you can do anything with the $newpost object you just created
// 
// End of your custom code

$post_title = get_the_title( $post_id );
$post_url = get_permalink( $post_id );
$subject="A post has been updated";

$message = "A post has been updated on your website:\n\n";
$message .= $post_title . ": " . $post_url;

// Send email to admin.
wp_mail( '[email protected]', $subject, $message );
}
add_action( 'save_post', 'my_project_updated_send_email' );

I hope this helps.