A CORE user with access to the Time & Expense features can only see the screens related to time entries, but not the Expense Entries screen.
This can happen if the user's security permissions restrict access to the Expense Entries screen. Your CORE administrator can change the security settings for that user so as to allow access to that screen. In particular, you can assign the Time & Expense security profile to the user in Employees > General > Details or from the Security screen by selecting the user and clicking on Actions > Assign Profile. Check CORE Help Center for details on assigning security profiles. Please check with your Sales Account Manager to purchase the required subscriptions.