The most common and most likely answer to this crossword clue is the 7 letter word PANTING
I've seen this crossword clue in The Daily Telegraph
P
A
N
T
I
N
G
Buddy explains!

The straight part
We know that "Out of breath" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case out of breath = panting.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 PANTING mean?
PANTING verb- To breathe quickly or in a labored manner, as after exertion or from eagerness or excitement; to respire with heaving of the breast; to gasp.
- To long eagerly; to desire earnestly.
- To long for (something); to be eager for (something).
- Of the heart, to beat with unnatural violence or rapidity; to palpitate.
- To sigh; to flutter; to languish.
- To heave, as the breast.
- To bulge and shrink successively, of iron hulls, etc.
- The act of one who pants.