The new Google Maps has been available for users to try out for a while now and there is no doubt it is missing a lot of legacy features from the old Google Maps - but there are also a lot of changes to how to access some features.
One such feature is accessing your "starred locations" or "my places" in Google Maps Mobile. It is such a common question that Abby D. from Google posted a thread just on that topic in the Google Maps Help forums.
I'd like to share a tip with you on how to access your starred locations in the new Google Maps mobile app. To access your starred locations, go to your profile --> Saved places --> View all. Your profile is the little person icon at the top of Maps, to the right of the search bar.
Similar to how you access your starred places in the new Google Maps by clicking on your profile gear icon:
You can do so on the mobile version of Google Maps:
There are some reports of places that were saved not showing up on the mobile version. Google is looking into that.
Forum discussion at Google Maps Help.