The most common and most likely answer to this crossword clue is the 4 plus 8 letter word LIFE SENTENCE
I've seen this crossword clue in The Sunday Telegraph
L
I
F
E
S
E
N
T
E
N
C
E
More clues leading to the result LIFE SENTENCE
- Go, feeling one’s leaving for long time
- A few words on career, the most you can get out of a judge?
- Unlimited time to append a few words to biography
- Feel intense cold when out? Stay inside for a long time
- No getting out of it?
- Magazine has a few words on severe punishment
- Biography with some text that’s appropriate for killer
- Time for a few words about oneself?
- A few words on mislaid file and a pronouncement from judge
- Part of a convict’s biography?
Buddy explains!

The straight part
We know that "that’s appropriate for killer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s appropriate for killer = life sentence.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.