The most common and most likely answer to this crossword clue is the 8 plus 7 letter word DOMESTIC ANIMALS
I've seen this crossword clue in The Guardian
D
O
M
E
S
T
I
C
A
N
I
M
A
L
S
More clues leading to the result DOMESTIC ANIMALS
Buddy explains!
The straight part
We know that "Pets possibly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pets possibly = domestic animals.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.