The most common and most likely answer to this crossword clue is the 9 letter word CANOODLES
I've seen this crossword clue in The Times
C
A
N
O
O
D
L
E
S
More clues leading to the result CANOODLES
Buddy explains!

The straight part
We know that "pets" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pets = canoodles.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 CANOODLES mean?
CANOODLES noun- A cuddle, hug, or caress
- To caress, pet, feel up, or make love.
- To cajole or persuade.