Once a work item has been created, it's not possible to apply another template to that work item.
While work items are not transferrable in this way, you can create a work item from the desired template, then copy the tasks from the previous work item to the new one.
Step 1: Create a new work item off of the desired template
Step 2: Go to your original work item, go into the work header options menu (...), choose 'Copy Tasks', then choose your new work item. If there are any emails and notes on the timeline that you'd like carried over you can move them to the new work item as well.
Step 3: Delete the original work item.
Keep in mind this will permanently remove the work from your account and have the following consequences:
All emails attached to the work will still be available in the contact(s) timelines.
Notes that were not assigned to anyone will be deleted.
Tasks will be deleted.
Please note that by deleting work, you are not deleting the schedule of work.