Users can check their progress in the "Open Timesheets" Lightning component.

Open Timesheets

It shows the recent weeks or months with the time entered and submitted so far.

- the Entered column shows entered and rejected hours

- the Submitted column shows the submitted and approved hours

The objective of the user would be to have 0 in the Entered hours (i.e. where he/she needs to do something)
and all time in the Submitted column (i.e. nothing for the user to do).

Just add the component, e.g. to the Home Page:

    - Setup Gear > Setup Page

    -- drag the "Open Timesheets" component to the page.

In the Open Timesheets property panel, you can select how many weeks/months to show - and if you want to show billable hours.

Open Timesheets Setup

When you de-select the "Show Own Timesheet" option and if on the Resource of the user, the field "Manager" is selected, the time information of people the user has access to is displayed.

Open T+E Reports

From the Resource Tab, you can also view Open Time Reports 

- Select a List View

- Optionally select Resources

- Select T+E Open Reports from the top right dropdown

The view shows the current and the last 3 weeks of time entered and the status - entered - submitted - approved.

You can also query specific Resource Groups.

When you click on the colored information, the Timesheet for that resource and that week is opened.

(this assumes that you have access to the user's T+E Items - see Enter Time for Others)