The most common and most likely answer to this crossword clue is the 5 plus 3 letter word SHRUG OFF
I've seen this crossword clue in Independent
S
H
R
U
G
O
F
F
More clues leading to the result SHRUG OFF
- Just ignore source of something unusually rough and loud
- Dismiss small rough unstable fellows
- Get rid of stylish rug, offered with reduction
- Get rid of unruly roughs following female
- Ignore hugs for emotional female
- Take no notice of outer garment being absent
- Disregard East Asian financier overwhelming under-graduate
Buddy explains!

The straight part
We know that "Get rid of" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case get rid of = shrug off.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.