The most common and most likely answer to this crossword clue is the 6 letter word BULBUL
I've seen this crossword clue in The Times
B
U
L
B
U
L
More clues leading to the result BULBUL
Buddy explains!
The straight part
We know that "A songbird" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a songbird = bulbul.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 BULBUL mean?
BULBUL noun- Any of several passerine songbirds, of the family Pycnonotidae (currently, 27 genera recognized), native to Africa and parts of Asia, sometimes known as the ‘nightingale of the East’.