The most common and most likely answer to this crossword clue is the 7 letter word ROSELLA
I've seen this crossword clue in The Times
R
O
S
E
L
L
A
More clues leading to the result ROSELLA
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 = rosella.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 ROSELLA mean?
ROSELLA noun- A parrot belonging to any of the five to eight species in the genus Platycercus (originally specifically Platycercus eximius) which is native to Australia and nearby islands.
- Hibiscus sabdariffa, an edible flower in the hibiscus family used to make hibiscus tea, also known as agua de jamaica or sorrel.