The most common and most likely answer to this crossword clue is the 4 plus 5 letter word TALL STORY
I've seen this crossword clue in The Sunday Telegraph
T
A
L
L
S
T
O
R
Y
More clues leading to the result TALL STORY
- Try to accept everyone’s for romance?
- Lie initially told every second by party supporter
- Everything extremely suspect in Conservative’s unlikely tale
- Incredible account of the giraffe?
- Fairytale with a giant?
- Socialist’s first to be embraced by lofty opponent? It’s hard to believe
- Party divided over shifting stall, can’t believe it!
- Stop a politician like in 19, it's unbelievable
- Sort and tally new boastful talk
- Stock not entirely in record? It's not quite believable
Buddy explains!

The straight part
We know that "Fairytale with a giant?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fairytale with a giant? = tall story.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.