The most common and most likely answer to this crossword clue is the 6 letter word COBWEB
I've seen this crossword clue in The Daily Telegraph
C
O
B
W
E
B
More clues leading to the result COBWEB
- Unfortunately, owe BBC for item of spin?
- We will probe company books finding evidence of neglect
- You and I chase horse hitched to black trap
- Novelist Jonathan takes in black and white book
- Network company books in which you and I will have entry
- Horse we start to brush shows signs of neglect
- Snare company partners entering the books
- Dicky bow in church? B___ fairy!
- Bread on internet? That will be a trap
- Fairy in a Shakespeare play, fine material
Buddy explains!

The straight part
We know that "Fairy in a Shakespeare play/fine material" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fairy in a shakespeare play/fine material = cobweb.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 COBWEB mean?
COBWEB noun- A spiderweb, or the remains of one, especially an asymmetrical one that is woven with an irregular pattern of threads.
- One of its filaments; gossamer
- Something thin and unsubstantial, or flimsy and worthless; valueless remainder.
- An intricate plot to catch the unwary
- A web page that either has not been updated for a long time, or that is rarely visited
- The European spotted flycatcher, Muscicapa striata.
- (usually in the plural) fuzzy inexact memories