Within Teamwork Chat, you can start a new conversation with another user on your account at any time.
In the left sidebar, select the People tab, and click on the name of the user to open a direct conversation window.
Alternatively, click the options (three dots) button in the top right corner of the sidebar, and select 'Create conversation' from the dropdown menu:
In the create conversation modal, just @mention the user you want to start a direct conversation with:
For more information, see: Creating a conversation/channel