The most common and most likely answer to this crossword clue is the 13 letter word THERMOPLASTIC
I've seen this crossword clue in The Times
T
H
E
R
M
O
P
L
A
S
T
I
C
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? = thermoplastic.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 THERMOPLASTIC mean?
THERMOPLASTIC noun- A plastic with this property.
- Softening when heated and hardening when cooled, and thus able to be moulded