Within Teamwork.com, you can set default task lists on your board columns.
When a default list is set, any new tasks added to the associated column in board view will be added to the task list.
Note: If you are using a modify task list trigger as well as a default task list, the trigger will override the default.

In the Board area of your project, Click the options button (three dots) to the right of the relevant column name and select Column Settings.

In the column settings, you can then select one of the project's active task lists as the default list for new cards.

Note: You can only add one task list as a default to a board column.
For more information, see: Using Default Board Columns in List View