The most common and most likely answer to this crossword clue is the 4 letter word AIRS
I've seen this crossword clue in The Daily Telegraph
A
I
R
S
More clues leading to the result AIRS
- Bald Cockney lacks any manners
- Country on the up? Why pulling out shows arrogance
- Eldest of children usually expressed pretentiousness
- Affectations in songs
- Songs written in couplets? Not initially
- Broadcasts put on by the pretentious
- Exposes pretentiousness
- Exposes bearings and relays, according to Roget
- Looks composed
- Pretentious songs?
Buddy explains!

The straight part
We know that "Pretentious/songs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pretentious/songs = airs.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 AIRS mean?
AIRS noun- The substance constituting earth's atmosphere, particularly:
- (usually with the) The apparently open space above the ground which this substance fills, formerly thought to be limited by the firmament but now considered to be surrounded by the near vacuum of outer space.
- A breeze; a gentle wind.
- A feeling or sense.
- A sense of poise, graciousness, or quality.
- (usually in the plural) Pretension; snobbishness; pretence that one is better than others.
- A song, especially a solo; an aria.
- Nothing; absence of anything.
- An air conditioner or the processed air it produces.
- Any specific gas.
- (motor sports) A jump in which one becomes airborne.
- A television or radio signal.
- Publicity.
- To bring (something) into contact with the air, so as to freshen or dry it.
- To let fresh air into a room or a building, to ventilate.
- To discuss varying viewpoints on a given topic.
- To broadcast (a television show etc.).
- To be broadcast.
- To ignore.