A winning song for one who might sing a lullaby (2,4)
I believe the answer is:
au pair
'one who might sing a lullaby' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'a winning song' is the wordplay.
'winning' becomes 'up' (eg being up at half time in football).
'song' becomes 'air' (air can mean a piece of music).
'a'+'up'+'air'='AU PAIR'
'for' is the link.
Can you help me to learn more?
(Other definitions for au pair that I've seen before include "Foreign home helper" , "child-minder" , "Young foreigner living with a family in return for housework" , "Foreign helper for room and board" , "Suddenly lose one's self-control" .)