From Longman Dictionary of Contemporary Englishpress baronˈpress ˌbaron noun [countable] British English BBCTCNsomeone who owns and controls one or more important national newspapers
Examples from the Corpus
press baron• A press baron is an immensely powerful figure.From Longman Business Dictionarypress baronˈpress ˌbaron (also media baron) someone who owns several newspapers and is therefore important and has a lot of influence → baron 