The most common and most likely answer to this crossword clue is the 3 letter word BIO
I've seen this crossword clue in The Daily Telegraph
B
I
O
More clues leading to the result BIO
Buddy explains!

The straight part
We know that "brief history" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case brief history = bio.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 BIO mean?
BIO noun- Biographical sketch
- Bioscope; cinema
- Biological.
- A person's life story, especially one published.
- The art of writing this kind of story.
- The study of all life or living matter.
- The living organisms of a particular region.
- The structure, function, and behavior of an organism or type of organism.