The most common and most likely answer to this crossword clue is the 9 letter word HYPERLINK
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More clues leading to the result HYPERLINK
Buddy explains!

The straight part
We know that "connection on-line" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case connection on-line = hyperlink.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 HYPERLINK mean?
HYPERLINK noun- Some text or a graphic in an electronic document that can be activated to display another document or trigger an action.
- (by extension) An address, URL, or program that defines a hyperlink's function.
- (of a hypertext document) To point to another document by a hyperlink.
- To add a hyperlink to a document.
- To use a hyperlink to jump to a document.