The most common and most likely answer to this crossword clue is the 6 letter word OBERON
I've seen this crossword clue in Financial Times
O
B
E
R
O
N
More clues leading to the result OBERON
- King in play destroying Borneo
- King in robe twirling about
- Honour King working a role in AMND
- Spirited king serious, on having lost crown
- Fairy king and queen embraced by retired aristocrat with love
- Medal possibly trendy for king of literature
- King giving order to man
- My boss during October only
- Shakespearean character close to one month on
- Dream king who is from Borneo
Buddy explains!

The straight part
We know that "Shakespearean character" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shakespearean character = oberon.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.