Algol Plus Ltd

You should do these actions 

1. Install/activate plugin https://wordpress.org/plugins/woocommerce-eu-vat-assistant/

2. Visit >WooCommerce>Phone Orders>Settings>Customers and  mark checkbox "Show field "VAT Number"

3. Add following PHP  code to functions.php(child theme!)  OR using plugin https://wordpress.org/plugins/code-snippets/

// Before using this code you must 
// - install https://wordpress.org/plugins/woocommerce-eu-vat-assistant/
// - mark "Show field Vat Numbe"  in  >Phone Orders>Settings>Customers
add_filter( 'wpo_after_update_customer', function($customer, $request ){
 if($customer['custom_fields']['vat_number']  AND class_exists("Aelia\WC\EU_VAT_Assistant\EU_VAT_Validation") ) {
  $vat_number = $customer['custom_fields']['vat_number'];
  $customer_country = substr($vat_number,0,2);
  $shop_country = WC_Countries::get_base_country();
  $validation = Aelia\WC\EU_VAT_Assistant\EU_VAT_Validation::factory();
  $raw_vat_validation_response = $validation->validate_vat_number($customer_country, $vat_number);
  if($raw_vat_validation_response['valid'] == true) {
    /* An EU customer will be considered exempt from VAT if:
      * - He is located in a country different from shop's base country.
      * - He is located in the same country as the shop, and option "remove VAT
      *   when customer in located in shop's base country" is enabled.
      */
    if( ($customer_country != $shop_country) || Aelia\WC\EU_VAT_Assistant\WC_Aelia_EU_VAT_Assistant::settings()->get(Aelia\WC\EU_VAT_Assistant\Settings::FIELD_REMOVE_VAT_IF_CUSTOMER_IN_BASE_COUNTRY) ) {
      $customer['is_vat_exempt']= true;
    }
  }  
  else {
    $customer['is_vat_exempt']= false;
    //rebuld HTML, mark in red
    $customer['formatted_billing_address']  = preg_replace( '#>Vat number: (.*?)<#s', '>Vat number: <span class="wpo_custom_field required-field">' . $customer['custom_fields']['vat_number'] . '</span><',  $customer['formatted_billing_address']);
  }  
 }
 return $customer;
},10,2);