The most common and most likely answer to this crossword clue is the 7 letter word AIR-DRY
A
I
R
-
D
R
Y
Buddy explains!
The straight part
We know that "purpose of a clothesline" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case purpose of a clothesline = air-dry.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 AIR-DRY mean?
AIR-DRY verb- To dry by exposure to the air.
- Free of moisture to the degree possible by exposure to air; "naturally" dried.