The most common and most likely answer to this crossword clue is the 8 letter word NOBBLING
I've seen this crossword clue in The Times
N
O
B
B
L
I
N
G
More clues leading to the result NOBBLING
Buddy explains!

The straight part
We know that "Getting at" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case getting at = nobbling.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 NOBBLING mean?
NOBBLING verb- To injure or obstruct intentionally.
- To gain influence by corrupt means or intimidation.
- To steal.
- To tamper (typically with a racehorse) in order to prevent from winning a race