Under Global Settings > Time & Expenses, there are rules that allow you to auto approve time entries for projects and employees. If you have 'Auto approve time entries for projects' checked, Core ensures that time entries get automatically approved for all new projects. For existing projects, you have to enable the rule from the Project Assignments > Rules screen.
If 'Auto approve time entries for employees' is checked, time entries logged by all new employees are automatically approved. If you want this to apply to existing employees, you need to check the 'Auto approve time' option from the Employees > General > Rates & Options screen.