The most common and most likely answer to this crossword clue is the 10 letter word BUDGERIGAR
I've seen this crossword clue in The Daily Telegraph
B
U
D
G
E
R
I
G
A
R
More clues leading to the result BUDGERIGAR
- Chirpy Australian doctor on a run after shift
- One moving to invest capital has billed companion?
- Chirpy character has to fix car that won't start after shift
- Maybe one moving round capital city gets the bird
- Australian flyer has to shift equipment by air without one
- One tweets: “Shift European capital — opening for reinvestment”
- Move to European capital and run into bird
- Shift capital and run, getting a flyer
- Shift gear with artist backing little singer
- Bird, one moving round capital
Buddy explains!

The straight part
We know that "flyer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case flyer = budgerigar.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 BUDGERIGAR mean?
BUDGERIGAR noun- A species of small parakeet native to Australia and often kept as pets, Melopsittacus undulatus.