Billy — perhaps initially the best ever (4)
I believe the answer is:
goat
This clue is a double definition.
'billy perhaps' is the first definition.
(billy goat)
'initially the best ever' is the second definition.
(GOAT can mean Greatest Of All Time)
(Other definitions for goat that I've seen before include "Domesticated animal supplying milk, meat and wool" , "lecher" , "Butting nanny, perhaps?" , "Horned beast" , "Beast (of Capricorn)" .)