Girl's head coming through as newborn appears — push gently! (5)
I believe the answer is:
nudge
'push gently' is the definition.
(I've seen this in another clue)
'girl's head coming through as newborn' is the wordplay.
'head' indicates taking the first letters.
'coming through' indicates putting letters inside.
'as newborn' becomes 'nude'.
The initial letter of 'girl' is 'g'.
'g' inserted inside 'nude' is 'NUDGE'.
'appears' is the link.
(Other definitions for nudge that I've seen before include "Remind, prompt gently" , "A gentle reminder?" , "Encouraging prompt" , "Jostle" , "Jogger" .)