The most common and most likely answer to this crossword clue is the 10 letter word BODY-CURER
I've seen this crossword clue in The Guardian
B
O
D
Y
-
C
U
R
E
R
Buddy explains!
The straight part
We know that "Shakespearean doctor" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shakespearean doctor = body-curer.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.