The most common and most likely answer to this crossword clue is the 4 plus 4 letter word VERA LYNN
I've seen this crossword clue in Independent
V
E
R
A
L
Y
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N
More clues leading to the result VERA LYNN
- Very nearly new name, 1/100
- Singer very nearly changed name
- A clergyman returns to Norfolk town briefly to see singing dame
- National treasure very nearly upset navy
- Forces sweetheart into empty van – nearly insane
- Singer’s very nearly changed name
- Victor nearly messed up embracing new sweetheart among the troops
Buddy explains!

The straight part
We know that "singing dame" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case singing dame = vera lynn.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.