The most common and most likely answer to this crossword clue is the 6 letter word PAUSES
I've seen this crossword clue in The Guardian
P
A
U
S
E
S
Buddy explains!

The straight part
We know that "stops to draw breath" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case stops to draw breath = pauses.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 PAUSES mean?
PAUSES noun- A button whose functions are pausing and resuming something, such as a DVD player, a video game or a computer.
- A temporary stop or rest; an intermission of action; interruption; suspension; cessation.
- A short time for relaxing and doing something else.
- Hesitation; suspense; doubt.
- In writing and printing, a mark indicating the place and nature of an arrest of voice in reading; a punctuation mark.
- A break or paragraph in writing.
- A sign indicating continuance of a note or rest.
- (as direct object) take pause: hesitate; give pause: cause to hesitate
- To take a temporary rest, take a break for a short period after an effort.
- To interrupt an activity and wait.
- To hesitate; to hold back; to delay.
- To halt the play or playback of, temporarily, so that it can be resumed from the same point.
- To consider; to reflect.