The most common and most likely answer to this crossword clue is the 7 letter word UNDATED
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More clues leading to the result UNDATED
Buddy explains!

The straight part
We know that "evergreen" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case evergreen = undated.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 UNDATED mean?
UNDATED adjective- Not marked with a date.
- Of a style that will not go out of fashion; a classic.
- Rising and falling in waves toward the margin, as a leaf; waved.