The most common and most likely answer to this crossword clue is the 8 letter word LORIKEET
I've seen this crossword clue in Financial Times
L
O
R
I
K
E
E
T
Buddy explains!
The straight part
We know that "parrot" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case parrot = lorikeet.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 LORIKEET mean?
LORIKEET noun- Any of various small, brightly coloured parrots native to Australasia. They are usually classified in the subfamily Loriinae.