The most common and most likely answer to this crossword clue is the 7 plus 8 letter word HEARSAY EVIDENCE
I've seen this crossword clue in Financial Times
H
E
A
R
S
A
Y
E
V
I
D
E
N
C
E
Buddy explains!
The straight part
We know that "second-hand account" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case second-hand account = hearsay evidence.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.