The most common and most likely answer to this crossword clue is the 4 plus 3 letter word MILK BAR
M
I
L
K
B
A
R
Buddy explains!
The straight part
We know that "Alcoholic-free establishment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case alcoholic-free establishment = milk bar.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.