Within Teamwork, you can choose a user on your project to be the project owner.
Note: The project owner feature is available on paid Teamwork subscription plans (excluding legacy Personal and Startup plans).
Adding a project owner allows your team to have a clear point of contact for the project. A project owner can be set from multiple areas of your project.
Dashboard
Go to the Dashboard area of your project and open the project details pane on the left.

Note: Only project administrators and site administrators can set and update the project owner.
Click the Not set option under Project Owner in the project details pane.

You can then choose an existing member of the project from the dropdown menu to assign as the owner. Click Update Owner to save your changes.
Note: Observers and collaborators on a project cannot be made a project owner.

The new project owner will be shown in the left pane. When an owner is already set, click the user's name to change the chosen owner.

Project options menu
Click the options button (three dots) to the right of the project name while viewing an individual project.
From the Manage Project subsection of the project options menu, hover over More Options and select Set Owner.

A pop-up modal will open where you can select a new owner for the project. Click Update Owner to apply the change.

Project settings
You can also update the project owner via the General tab of the project's settings area.

Hover over the project owner field and click the edit pencil. You can then select a new project owner from the dropdown.

Creating a project
You can also set a project owner when you first create a project, under the People tab. The user(s) selected to be added to the project will be listed in the Project Owner dropdown at the bottom.

For more information, see: Adding Project Updates