The most common and most likely answer to this crossword clue is the 6 letter word HECKLE
I've seen this crossword clue in The Guardian
H
E
C
K
L
E
More clues leading to the result HECKLE
- Disruptive cheek hampering foremost of luvvies?
- Outrageous cheek without unqualified driver getting to shout abusively
- Shout down my left ear at first
- Outburst of cheek cramping lecturer?
- I’m surprised line’s lost in taunting remark
- Goodness, the French interrupt rudely
- Jeer abusively man, clerk that’s awkward right away
- Heavens! The French abuse a speaker
- Interrupt speech with diabolical cheek about line
- Dearie me! The French are to barrack
Buddy explains!

The straight part
We know that "Shout down" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shout down = heckle.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 HECKLE mean?
HECKLE noun- An instrument with steel pins used to comb out flax or hemp.
- (usually now in the plural) One of the long, narrow feathers on the neck of birds, most noticeable on the rooster.
- A feather used to make a fishing lure or a fishing lure incorporating a feather.
- (usually now in the plural) By extension (because the hackles of a rooster are lifted when it is angry), the hair on the nape of the neck in dogs and other animals; also used figuratively for humans.
- A plate with rows of pointed needles used to blend or straighten hair.
- A feather plume on some soldier's uniforms, especially the hat or helmet.
- Any flimsy substance unspun, such as raw silk.
- The long shining feathers on a cock's neck.
- A feather ornament in the full-dress bonnets of Highland regiments.
- To question harshly in an attempt to find or reveal weaknesses.
- To insult, tease, make fun of or badger.
- To prepare flax for spinning using special combs called hackles