The most common and most likely answer to this crossword clue is the 8 plus 4 letter word MORALITY PLAY
I've seen this crossword clue in The Daily Telegraph
M
O
R
A
L
I
T
Y
P
L
A
Y
More clues leading to the result MORALITY PLAY
Buddy explains!
The straight part
We know that "bit of old-fashioned drama" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bit of old-fashioned drama = morality play.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.