The most common and most likely answer to this crossword clue is the 11 letter word HANDSHAKING
I've seen this crossword clue in The Daily Telegraph
H
A
N
D
S
H
A
K
I
N
G
Buddy explains!
The straight part
We know that "establishing a connection" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case establishing a connection = handshaking.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 HANDSHAKING mean?
HANDSHAKING verb- To perform a handshake; to shake hands.
- To perform a handshake with another device.
- A greeting by clasping hands.
- A step in a protocol in which information is exchanged between computing processor devices; often as part of the initiation process for communications.