The most common and most likely answer to this crossword clue is the 6 letter word BARBET
I've seen this crossword clue in The Times
B
A
R
B
E
T
Buddy explains!
The straight part
We know that "Songbird" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case songbird = barbet.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 BARBET mean?
BARBET noun- Any of numerous arboreal birds of the families Capitonidae, Lybiidae, and Megalaimidae, within the order Piciformes.
- A dog of a small-bodied breed with long curly hair.
- A larva that feeds on aphids.