The most common and most likely answer to this crossword clue is the 7 letter word REQUEST
I've seen this crossword clue in The Times
R
E
Q
U
E
S
T
Buddy explains!
The straight part
We know that "Petition" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case petition = request.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 REQUEST mean?
REQUEST noun- Act of requesting (with the adposition at in the presence of possessives, and on in their absence).
- A formal message requesting something.
- Condition of being sought after.
- A message sent over a network to a server.
- That which is asked for or requested.
- To ask for (something).
- To ask (somebody) to do something.