The most common and most likely answer to this crossword clue is the 13 plus 4 letter word FISH-AND-CHIP SHOP
I've seen this crossword clue in The Times
F
I
S
H
-
A
N
D
-
C
H
I
P
S
H
O
P
Buddy explains!
The straight part
We know that "battering Establishment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case battering establishment = fish-and-chip shop.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.