modify-woo-new-order-notification.php

<?php

/**
 * Adding [Urgent] to email subject if free shipping method woocommerce
 */

add_filter('woocommerce_email_subject_new_order', 'change_admin_email_subject', 1, 2);

function change_admin_email_subject( $subject, $order ) {
	global $woocommerce;

  $blogname = wp_specialchars_decode(get_option('blogname'), ENT_QUOTES);

  //Check if shipping method exist.
  if($order->get_shipping_method()){

    //Get shipping name ref: https://stackoverflow.com/a/26174867
    $shipping = reset( $order->get_items( 'shipping' ) )->get_method_id();
  }

  // Modify the subject if it is free shipping
  if( isset( $shipping ) && $shipping === 'free_shipping'){
    $subject = sprintf( '[URGENT] - [%s] New Customer Order (# %s) from Name %s %s', $blogname, $order->id, $order->billing_first_name, $order->billing_last_name );
  }else{
    // Default subject
    $subject = sprintf( '[%s] New Customer Order (# %s) from Name %s %s', $blogname, $order->id, $order->billing_first_name, $order->billing_last_name );
  }

  return $subject;
  
}