In Core, you can delete an employee record or any other record typically by going to its list view and selecting Delete from it row action menu. You can also delete multiple records in bulk by selecting them on the grid and then clicking Actions > Delete. However, deleting an employee or any other item is not allowed if it has dependencies or transactions associated.
In this case, if you are deleting an employee having time and expense entries associated, you will get an error suggesting making the employee inactive instead. You cannot delete employees who have already recorded time or expense entries. You can either change their status to Inactive or Terminated if you no longer want to see them in the drop-down lists or screens. Alternatively, you can delete those time and expenses first and any other associations, if possible, and then delete the employee. Check the Core Help for details.