Вам нужно добавить android:fitsSystemWindows="true"
к android.support.v4.widget.DrawerLayout
и android.support.design.widget.NavigationView
.
Например, код будет выглядеть как
<?xml version="1.0" encoding="utf-8"?>
<!-- Use DrawerLayout as root container for activity -->
<android.support.v4.widget.DrawerLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
android:id="@+id/drawer_layout"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:fitsSystemWindows="true">
<!-- Layout to contain contents of main body of screen (drawer will slide over this) -->
<FrameLayout
android:id="@+id/content_frame"
android:layout_width="match_parent"
android:layout_height="match_parent" />
<!-- Container for contents of drawer - use NavigationView to make configuration easier -->
<android.support.design.widget.NavigationView
android:id="@+id/nav_view"
android:layout_width="wrap_content"
android:layout_height="match_parent"
android:layout_gravity="start"
android:fitsSystemWindows="true" />
</android.support.v4.widget.DrawerLayout>
И вывод будет похож (как чтовам нужно)