The most common and most likely answer to this crossword clue is the 4 letter word FADO
F
A
D
O
Buddy explains!
The straight part
We know that "dejected air" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dejected air = fado.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 FADO mean?
FADO noun- A Portuguese folk song, usually featuring a single vocalist, Portuguese guitar and sometimes classical guitar. Lyrical themes are often melancholic in nature; the structure of the song is of greater importance.