The most common and most likely answer to this crossword clue is the 13 letter word COUNTER-TENOR
I've seen this crossword clue in The Guardian
C
O
U
N
T
E
R
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T
E
N
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R
Buddy explains!
The straight part
We know that "A singing bank teller" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a singing bank teller = counter-tenor.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 COUNTER-TENOR mean?
COUNTER-TENOR noun- Adult male singer who uses head tone or falsetto to sing far higher than the typical male vocal range
- Male singing voice far higher than the typical male vocal range
- (Older) a part or section performing a countermelody against the tenor or main part