Spur (on)
(Other definitions for egg that I've seen before include "Rasher to go with this" , "Quiche ingredient" , "Baby carrier?" , "Item with a yolk" , "Cooked breakfast staple" .)
'spur on' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for encourage that I've seen before include "Spur on, inspire" , "Hearten, foster" , "Give support, confidence or hope to" , "Give hope to (someone)" , "Motivate" .)
(Other definitions for forward that I've seen before include "Attacking player" , "Fresh" , "Presumptuous" , "advance" , "Bold, overfamiliar" .)