The most common and most likely answer to this crossword clue is the 7 letter word TIEBACK
I've seen this crossword clue in Financial Times
T
I
E
B
A
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K
More clues leading to the result TIEBACK
Buddy explains!

The straight part
We know that "fabric which secures curtains" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fabric which secures curtains = tieback.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 TIEBACK mean?
TIEBACK noun- A loop of cloth, cord, etc., which is placed around a curtain to hold it open to one side.
- A newspaper rewrite or short synopsis of the information presented in the original story. in order to refresh the memories of readers who saw the old story and to update new readers.