Thank you for approaching us.
Yes, you can create another project to capture work on a different task.
Creating another project and task for a different department will not hamper your current project schedule and also, it would help the user to capture proper hours for the other task. It will be in a totally different space, but the total work captured by that user in both the projects will be displayed within the same Account Timesheet, so that the total hours captured by that user would not be lost.
If you are facing any other issues, Please feel free to contact us. We are happy to help you.