The most common and most likely answer to this crossword clue is the 9 letter word REMEMBERS
R
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Buddy explains!

The straight part
We know that "Doesn't forget" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case doesn't forget = remembers.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 REMEMBERS mean?
REMEMBERS verb- To reconstitute or reassemble that which has been dismembered.
- To recall from one's memory; to have an image in one's memory.
- To memorize; to put something into memory.
- To keep in mind, be mindful of
- To not forget (to do something required)
- To convey greetings from.
- To put in mind; to remind (also used reflexively)
- To engage in the process of recalling memories.
- To give (a person) money as a token of appreciation of past service or friendship.
- To commemorate, to have a remembrance ceremony