The most common and most likely answer to this crossword clue is the 4 letter word WIKI
I've seen this crossword clue in The Times
W
I
K
I
Buddy explains!
The straight part
We know that "Website inviting knowledgeable improvements, primarily?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case website inviting knowledgeable improvements, primarily? = wiki.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 WIKI mean?
WIKI noun- A collaborative website which can be directly edited merely by using a web browser, often by anyone with access to it.
- To research on Wikipedia or some similar wiki.
- To contribute to a wiki.
- To participate in the wiki-based production of.