Young bird starts to emerge after goose lays egg on time (6)
I believe the answer is:
eaglet
'young bird' is the definition.
(eaglet is a kind of young bird)
'starts to emerge after goose lays egg on time' is the wordplay.
'starts to' indicates taking the first letters.
'on' is a charade indicator (letters next to each other).
'time' becomes 't'.
The first letters of 'emerge after goose lays egg' is 'eagle'.
'eagle'+'t'='EAGLET'
(Other definitions for eaglet that I've seen before include "Little bird" , "Young lawyer" , "Get ale for the young bird" , "Young keen-sighted bird" , "Eyrie resident" .)