Ah, okay. The system will alert the Assigned Team if it's overdue but someone from the Department/Team will need to manually re-assign to someone else as we don't have automatic actions at this time. Everything is pretty much manual except when using Ticket Filters (which only execute on opening new tickets).
If you don't want to do it like this then there is no way to accomplish this with vanilla osTicket. You will need to modify the code to your liking. As with all customizations, you are on your own.