The most common and most likely answer to this crossword clue is the 5 plus 5 letter word PRESS BARON
I've seen this crossword clue in The Guardian
P
R
E
S
S
B
A
R
O
N
More clues leading to the result PRESS BARON
- Media mogul to continue drinking in pub
- Iron Duke’s hierarchical inferior, a media tyrant
- Like Lord Copper to continue to obstruct the legal profession
- Enforce restriction against Beaverbrook?
- Paper supplier appears as crowd stop working
- Newspaper mogul to continue energetically, circumventing prohibition
Buddy explains!
The straight part
We know that "a media tyrant" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a media tyrant = press baron.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.