The most common and most likely answer to this crossword clue is the 8 letter word FACEBOOK
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More clues leading to the result FACEBOOK
Buddy explains!

The straight part
We know that "Website" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case website = facebook.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 FACEBOOK mean?
FACEBOOK verb- To use the social-networking site Facebook.
- To send a message or leave a comment on Facebook.
- A reference book or electronic directory made up of individuals’ photographs and names.
- A college publication distributed at the start of the academic year by university administrations with the intention of helping students get to know each other better.