Quiet infant (not the first born); this must have worked! (7)
I believe the answer is:
lullaby
'born this must have worked' is the definition.
The definition suggests a singular noun which matches the answer.
'quiet infant not the first' is the wordplay.
'quiet' becomes 'lull' ('lull' can be a synonym of 'quiet'**).
'infant' becomes 'baby' ('baby' can be a synonym of 'infant').
'not the first' means to remove the first letter.
'baby' with its first letter taken away is 'aby'.
'lull'+'aby'='LULLABY'
(Other definitions for lullaby that I've seen before include "Soothing song for child" , "Soothing song for infants" , "Soothing song for baby - Brahms wrote a good one" , "Cradle song" , "Cradle-song" .)