Typically, you need the Manager subscription to review and approve time and expense entries of your employees. It includes access to the Time & Expense Reviewer, which is the recommended screen to review and approve time and expenses. Check the Core Help for details.
The ability to approve your own time is present in the Time & Expense subscription, but if you want to prevent employees from approving their own time, you should customize their security permissions to un-check Allow Approve My Entries in Security > Customize/Edit Profile > Time Entry. Check the Core Help for details.
If you want to allow Time & Expense users to approve the time entries of other users on the projects they manage, you can customize their security permissions and check Allow access to entries of all employees and Allow to approve entry in Security > Customize/Edit Profile > Time Entry. Additionally, you can also un-check the option Allow access only to entries of projects I manage if you want the users to access the entries of even those projects that they don't manage. Check the Core Help for details on customizing security permissions.