The most common and most likely answer to this crossword clue is the 10 letter word FUNNEL-WEB
I've seen this crossword clue in Financial Times
F
U
N
N
E
L
-
W
E
B
Buddy explains!

The straight part
We know that "spider" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case spider = funnel-web.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.