The most common and most likely answer to this crossword clue is the 3 letter word INS
I
N
S
More clues leading to the result INS
Buddy explains!

The straight part
We know that "connections" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case connections = ins.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 INS mean?
INS noun- A position of power or influence, or a way to get it.
- (chiefly in the plural) One who, or that which, is in; especially, one who is in office.
- The state of a batter/batsman who is currently batting; see innings.
- A re-entrant angle; a nook or corner.
- Abbreviation of inch; inches.
- Insert