One way to do this is to set up this Zendesk - Campaign Monitor integration. It will automatically create a Campaign Monitor contact for new Zendesk tickets created. This way, you can ensure that each customer who contacts you will receive a prompt and professional response.
Additionally, it can help to build relationships with your customers and create loyalty. So if you're looking for ways to improve your customer service, setting up Campaign Monitor contacts for every Zendesk ticket is a great place to start.