The most common and most likely answer to this crossword clue is the 9 letter word FAVOURITE
I've seen this crossword clue in The Daily Telegraph
F
A
V
O
U
R
I
T
E
Buddy explains!
The straight part
We know that "pet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pet = favourite.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 FAVOURITE mean?
FAVOURITE noun- A person or thing who enjoys special regard or favour.
- A person who is preferred or trusted above all others.
- A contestant or competitor thought most likely to win.
- A bookmark in a web browser.
- (in the plural) A short curl dangling over the temples, fashionable in the reign of Charles II.
- To favour.
- To bookmark.
- To add to one's list of favourite items on a website that allows users to compile such lists.
- Preferred or liked above all others (unless qualified).
- Belonging to a category whose members are all preferred or liked over nonmembers.