The most common and most likely answer to this crossword clue is the 7 plus 8 letter word NOTHING PERSONAL
I've seen this crossword clue in The Daily Telegraph
N
O
T
H
I
N
G
P
E
R
S
O
N
A
L
More clues leading to the result NOTHING PERSONAL
Buddy explains!

The straight part
We know that "don’t take offence" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case don’t take offence = nothing personal.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.