The most common and most likely answer to this crossword clue is the 9 letter word BRIQUETTE
I've seen this crossword clue in The Times
B
R
I
Q
U
E
T
T
E
Buddy explains!

The straight part
We know that "Fire-starter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fire-starter = briquette.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.
What does BRIQUETTE mean?
BRIQUETTE noun- A small brick, typically made of charcoal and used for fuel.
- A block of artificial stone in the form of a brick, used for paving.
- A moulded sample of solidified cement or mortar for use as a test piece for showing the strength of the material.
- A cigarette lighter.
- To form (coal, etc.) into small bricks.