The most common and most likely answer to this crossword clue is the 5 letter word PLEAD
I've seen this crossword clue in The Daily Telegraph
P
L
E
A
D
More clues leading to the result PLEAD
- Beg Penny to go first
- Petition putting pressure on chief
- Pressure to spearhead appeal
- What defendants do first, after start of proceedings
- Beg quietly to be given a major part
- ‘Phosphorus’!? Offer something in excuse!
- Pastor gets usher to beg
- Beg pusher
- An apple a day keeps this, I pray
- Beg with quiet restraint
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 = plead.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 PLEAD mean?
PLEAD verb- To present (an argument or a plea), especially in a legal case.
- To beg, beseech, or implore.
- To offer by way of excuse.
- To discuss by arguments.