Crooner missing intro holds note for number (7)

I believe the answer is:
integer
'number' is the definition.
(synonyms)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for integer that I've seen before include "Gin tree (anag)" , "The whole thing" , "Say one" , "rational number remains" , "A whole number, not a fraction" .)
