The most common and most likely answer to this crossword clue is the 9 plus 7 letter word PRINCE OF DENMARK
I've seen this crossword clue in The Guardian
P
R
I
N
C
E
�
�
O
F
D
E
N
M
A
R
K
Buddy explains!
The straight part
We know that "Shakespearean role" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shakespearean role = prince of denmark.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.