The most common and most likely answer to this crossword clue is the 4 plus 4 letter word PUNK ROCK
I've seen this crossword clue in The Guardian
P
U
N
K
R
O
C
K
More clues leading to the result PUNK ROCK
Buddy explains!
The straight part
We know that "That’s anarchic!/That’s anarchic!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s anarchic!/that’s anarchic! = punk rock.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.