The most common and most likely answer to this crossword clue is the 7 letter word STEP-IN
I've seen this crossword clue in The Times
S
T
E
P
-
I
N
Buddy explains!
The straight part
We know that "that doesn't need fastening" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that doesn't need fastening = step-in.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 STEP-IN mean?
STEP-IN noun- (also in plural) An item of clothing which one steps into to put on; specifically, women's panties.