This functionality is already available in the PK4 TimeTracker application. Any updates or additions made to Projects, Tasks, and Work types in Salesforce will automatically reflect across all TimeTracker platforms, including Web, Mobile, and Salesforce apps.
If you find that you're unable to view new Projects, Tasks, or Work types in the drop-down menu, simply navigate back to the Jobs list within the application and return to the Check-In page. This action should enable you to see the recently added Projects, Tasks, or Work types.
Please note that the objects for tracking time in your organization may vary. The Administrator might have modified the configuration by removing Projects, Tasks, and Work types and choosing alternative objects for time tracking in your org.