The most common and most likely answer to this crossword clue is the 9 letter word HOMEWARDS
I've seen this crossword clue in The Guardian
H
O
M
E
W
A
R
D
S
More clues leading to the result HOMEWARDS
Buddy explains!
The straight part
We know that "where some pigeons are heading?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case where some pigeons are heading? = homewards.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 HOMEWARDS mean?
HOMEWARDS adjective- Of or pertaining to leading toward home.
- Towards home