There is no direct option in Core to set due dates for time and expense submission. However, as a workaround, you can create to-dos and assign them to employees. The End Date on the to-dos can act as a deadline for the employees to submit their time entries. The employees can even create time entries from these to-dos. Check the Core Help for more on that. You can also ask each employee to set reminders for themselves. Check the Core Help for more details.