The most common and most likely answer to this crossword clue is the 6 letter word HECTOR
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More clues leading to the result HECTOR
Buddy explains!

The straight part
We know that "Ancient hero/bully" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ancient hero/bully = hector.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.
What does HECTOR mean?
HECTOR noun- Sometimes in the form Hector: a blustering, noisy, turbulent fellow; a blusterer, bully.
- To dominate or intimidate in a blustering way; to bully, to domineer.
- To behave like a hector or bully; to bluster, to swagger; to bully.