The most common and most likely answer to this crossword clue is the 13 letter word BIBLE-BASHING
B
I
B
L
E
-
B
A
S
H
I
N
G
Buddy explains!
The straight part
We know that "strong words from the vicar" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case strong words from the vicar = bible-bashing.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.