Yes, you can! If you go in under "Profile" in the bottom right corner of the app, you will find the header "Notifications" in the "Settings" section. Here, you can turn on notifications for BookBeat as well as choose what kind of notifications you want to receive.
If you want to know immediately when an upcoming book you have saved is released for example, then turn on notifications up top and choose to receive notifications for "Upcoming Books".
If you cannot find the header "Notfications", you might have an older version of the BookBeat app. Try to update your app to the newest available version in that case.
Please observe that this feature is not available for iOS devices with an operative system older than iOS 13 or if you have a Huawei device without Google Play services.