The most common and most likely answer to this crossword clue is the 9 letter word CHRONICLE
I've seen this crossword clue in Financial Times
C
H
R
O
N
I
C
L
E
More clues leading to the result CHRONICLE
- Church function includes mostly pleasant historical record
- Awful content taken out of life story
- Very bad article in French account of past events
- Bad French article gives an account of events
- Account of severe gale missing first two parts
- Extremely little basis for appalling narrative
- Chapter, part containing good unfinished record of events
- Story about following river in stylish French article
- The Parisian follows deplorable account
- Story of church fellow in charge, having drink, losing head
Buddy explains!

The straight part
We know that "Account" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case account = chronicle.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 CHRONICLE mean?
CHRONICLE noun- A written account of events and when they happened, ordered by time.
- To record in or as in a chronicle.