The most common and most likely answer to this crossword clue is the 7 letter word AIRHOLE
I've seen this crossword clue in The Times
A
I
R
H
O
L
E
Buddy explains!

The straight part
We know that "Part of breathing apparatus" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of breathing apparatus = airhole.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 AIRHOLE mean?
AIRHOLE noun- A hole provided for ventilation or breathing.
- A hole in ice through which air escapes.
- An air pocket.