The most common and most likely answer to this crossword clue is the 6 letter word PARDON
I've seen this crossword clue in The Guardian
P
A
R
D
O
N
More clues leading to the result PARDON
- I didn't catch that mafioso after a number of shots
- Excuse made by average teacher at university
- Standard fellow, eh?
- Excuse average teacher
- I didn’t catch that release
- Excuse signal — charge to be overturned
- Standard dress in what?
- Withdrawing criminal charge, fellow shows forgiveness
- What‘s to forgive?
- Be merciful to average fellow
Buddy explains!

The straight part
We know that "I couldn’t hear" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case i couldn’t hear = pardon.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 PARDON mean?
PARDON noun- Forgiveness for an offence.
- An order that releases a convicted criminal without further punishment, prevents future punishment, or (in some jurisdictions) removes an offence from a person's criminal record, as if it had never been committed.
- To forgive (a person).
- To refrain from exacting as a penalty.
- To grant an official pardon for a crime.
- Often used when someone does not understand what another person says.