Sellers cannot contact new buyers. The only way to communicate with a buyer is if an order is initiated, a "Conversation" thread is created and you will be able to communicate with the buyer. You may also contact the buyer if the buyer contacts you first.
Note: If you previously completed an order for a buyer, you can access My Contacts to contact buyers. My Contacts enables you to keep in touch with Fiverr users you have interacted with in the past. Your contact lists display key interactions between you and your contact; the number of completed orders, the amount spent, when the last order was made, and a link to your Inbox conversation.