The most common and most likely answer to this crossword clue is the 4 letter word MYNA
I've seen this crossword clue in The Sunday Telegraph
M
Y
N
A
More clues leading to the result MYNA
- . Talkative bird belonging to the writer recalled article
- Talking bird many may climb up to see
- Bird able to speak, surprising many
- Flyer mailed, initially a single one returned
- Bird that’s surprising North America
- Imitating flier many reproduced
- Film industry in LA finally finds flapper who can speak
- Talkative bird‘s scrummy naughty bits
- Many disturbed by bird
- Mimic returned some money
Buddy explains!

The straight part
We know that "Imitating flier" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case imitating flier = myna.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 MYNA mean?
MYNA noun- One of the South and East Asian birds of the starling family Sturnidae.