The most common and most likely answer to this crossword clue is the 4 plus 3 plus 4 plus 3 letter word READ THE RIOT ACT
I've seen this crossword clue in The Daily Telegraph
R
E
A
D
T
H
E
R
I
O
T
A
C
T
More clues leading to the result READ THE RIOT ACT
Buddy explains!
The straight part
We know that "to make drastic threat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to make drastic threat = read the riot act.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.