HI Olivia,
The best option here would be to subscribe your Director to the tasks that they want to receive notifications for conversations on. You can read more about subscribing here.
Unfortunately, you're not able to add a subscription at the template level for it to auto-carry over onto projects. Unless you have Workfront Fusion, the project owner or Director would need to manually subscribe themselves to the tasks they wanted updates on. If you do have Fusion, however, this could be easily achieved. An automation could be developed that would watch for all new tasks with a specific template task ID and auto-subscribe people to those tasks.
Best Regards,
Rich.