The most common and most likely answer to this crossword clue is the 4 letter word LOUD
I've seen this crossword clue in The Times
L
O
U
D
More clues leading to the result LOUD
- Flamboyant old Law Lord entertains
- Deafening, behold, and extremely unbalanced
- Mouthy old dons judge addressed in court
- Love to interrupt law lord, flashy
- Flashy couple left, heading back
- Flashy student with Open University departs
- Large rotund regulars ignored forte
- Vulgar Conservative leaves a pall of gloom?
- F–flamboyant?
- Vulgar couple beginning to lech from behind
Buddy explains!

The straight part
We know that "Deafening" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case deafening = loud.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 LOUD mean?
LOUD noun- A loud sound or part of a sound.
- High-quality marijuana.
- (of a sound) Of great intensity.
- (of a person, thing, event, etc.) Noisy.
- (of a person, event, etc.) Not subtle or reserved, brash.
- (of clothing, decorations, etc.) Having unpleasantly and tastelessly contrasting colours or patterns; gaudy.
- (of marijuana) High-quality; premium; (by extension) having a strong or pungent odour indicating good quality
- Loudly.