Hide chats from your Recent tab by swiping to the left on the the contact and tapping the Delete icon.
You will have the options to Delete, Hide or Cancel. Choose Hide.
You can also tap Edit in the top left corner of your screen, select the contact, tap Delete in the bottom right of your screen, then from the options, choose Hide. The chat will then be removed from your Recent tab, but the chat conversation is still available. If you wish to remove all the contents of that chat, you’ll need to delete the entire chat history.