The most common and most likely answer to this crossword clue is the 7 letter word YAFFLES
I've seen this crossword clue in The Times
Y
A
F
F
L
E
S
Buddy explains!

The straight part
We know that "woodpeckers" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case woodpeckers = yaffles.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 YAFFLES mean?
YAFFLES noun- The European green woodpecker, Picus viridis.
- Of the green woodpecker: to make its distinctive cry.