You are given a specific hero for clearing certain chapters in the story mode.

Servant	How to unlock
Archer - David	Clear Third Singularity - Oceanus
Assassin - Henry Jekyll & Hyde	Clear Fourth Singularity - London
Berserker - Kiyohime	Clear First Singularity - Orleans
Caster - Cu Chulainn	Clear Singularity F - Fuyuki
Caster - Geronimo	Clear Fifth Singularity - E Pluribus Unum
Lancer - Jaguar Man	Clear Seventh Singularity - Babylonia
Rider - Boudica	Clear Second Singularity - Septem
Saber - Bedivere	Clear Sixth Singularity - Camelot