He’s come back with a fresh egg (4)
I believe the answer is:
owen
'he's' is the definition.
'come back with a fresh egg' is the wordplay.
'come back' says the letters should be written in reverse.
'with' says to put letters next to each other.
'a fresh' becomes 'new' (I've seen this before).
'egg' becomes 'o' (I've seen this in other clues).
'new'+'o' is 'newo'.
'newo' backwards is 'OWEN'.
(Other definitions for owen that I've seen before include "Wilfred -, English poet killed in World War One" , "Clive --, English actor" , "Former SDP leader" , "Welsh boy's name" , "'E won over the Welshman" .)