API could be consumed in many ways in Laravel. For e.g. you can create your own custom API Package to consume API on the remote application. Or there is a better way. This is by using the Guzzle HTTP Client.

1. First install Guzzle

//Specify Guzzle as a dependency in your project's existing composer.json file:

 {
   "require": {
      "guzzlehttp/guzzle": "~6.0"
   }
}

-> composer update

2. On your Laravel controller

use GuzzleHttp\Client as GuzzleHttpClient;
use GuzzleHttp\Exception\RequestException;

...

public function passwordHash()
{
      try {

           $client = new GuzzleHttpClient();

           $apiRequest = $client->request('GET', 'http://legacyapp.com/api/PasswordServiceAPI/hashPassword', [
                'query' => ['plain' => 'Ab1L853Z24N'],
               // 'auth' => ['John', 'password777'],       //If authentication required
               // 'debug' => true                                  //If needed to debug   
          ]);

          // echo $apiRequest->getStatusCode());
          // echo $apiRequest->getHeader('content-type'));

          $content = json_decode($apiRequest->getBody()->getContents());

      } catch (RequestException $re) {
          //For handling exception
      }
 }