The most common and most likely answer to this crossword clue is the 7 letter word ENTREAT
I've seen this crossword clue in The Times
E
N
T
R
E
A
T
More clues leading to the result ENTREAT
- Pray with heart not with head, returning thanks
- Implore centre attendant a bit
- Plea for short dash to provide medical help
- Printing space to handle petition?
- Pray to some in centre — atheists!
- Beg Parisian in hospital to abandon threat
- Petition that doctors threaten, saving hospital
- Plead with writer to remove page on pleasure excursion
- Beseech topless males to provide something for free
- Implore conservationists to step in before soldiers return
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 = entreat.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 ENTREAT mean?
ENTREAT noun- An entreaty.
- To treat with, or in respect to, a thing desired; hence, to ask for earnestly.
- To beseech or supplicate (a person); to prevail upon by prayer or solicitation; to try to persuade.
- To invite; to entertain.
- To treat or discourse; hence, to enter into negotiations, as for a treaty.
- To make an earnest petition or request.
- To treat, or conduct toward; to deal with; to use.