The most common and most likely answer to this crossword clue is the 6 letter word SISKIN
I've seen this crossword clue in The Guardian
S
I
S
K
I
N
More clues leading to the result SISKIN
Buddy explains!

The straight part
We know that "singer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case singer = siskin.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 SISKIN mean?
SISKIN noun- A small green and yellow European finch, Carduelis spinus spinus or Carduelis spinus, now Spinus spinus.
- Any of various similar birds in subfamily Carduelinae, principally in the genus Spinus.