The most common and most likely answer to this crossword clue is the 7 letter word JUNKING
I've seen this crossword clue in The Daily Telegraph
J
U
N
K
I
N
G
Buddy explains!

The straight part
We know that "Getting rid of" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case getting rid of = junking.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 JUNKING mean?
JUNKING verb- To throw away.
- To find something for very little money (meaning derived from the term junk shop)