This page discusses the removal of the Apache HTTP classes, and it suggests a workaround as well:
To continue using the Apache HTTP APIs, you must first declare the following compile-time dependency in your build.gradle file:
android { useLibrary 'org.apache.http.legacy' }
In my case Android Studio still complained that it couldn’t find these classes, but the app did build and run.
The page does recommend you move to HttpURLConnection, though.