The most common and most likely answer to this crossword clue is the 6 plus 3 plus 6 letter word BITING THE BULLET
I've seen this crossword clue in The Times
B
I
T
I
N
G
T
H
E
B
U
L
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T
Buddy explains!
The straight part
We know that "Through gritted teeth, accepting one’s been fired" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case through gritted teeth, accepting one’s been fired = biting the bullet.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.