A protogynous hermaphrodite is an animal that begins its life cycle as a female. As the animal ages, based on internal or external triggers, it shifts sex to become a male animal. Many fish, such as the gag grouper, undergo just such a metamorphosis. Male fecundity goes up greatly with age more than female's so makes sense to start off as a female and then turn into a male. Small males get very little reproductive success but as they grow they have better reproductive success.
For sea goldies, one of the females in the male's harem will undergo a sex reversal and become the male.
Protogynous hermaphrodites are quite common in the Anthiinae family.