This servants cannot be summoned by rolling until you clear the Singularity that locks them or they are in rate up (can only be summoned during their rate up until you clear the Singularity).

Unlockable	How to unlock
Artoria\Altria Pendragon (Alter\Saber)	Clear Fuyuki
Artoria\Altria Pendragon (Alter\Lancer)	Clear London
Artoria\Altria Pendragon (Lancer)	Clear Camelot
Bedivere (Saber)	Clear Camelot
Cu Chulainn (Alter\Berserker)	Clear E Pluribus Unum
Cu Chulainn (Caster)	Clear Fuyuki
Emiya (Alter\Archer)	Clear Shinjuku
Gawain (Saber)	Clear Camelot
Gilles De Rais (Caster)	Clear Órleans
Gorgon (Avenger)	Clear Babylonia
Jaguar Man (Lancer)	Clear Babylonia
Kato Danzo	Clear Shimosa
Li Shuwen (Lancer)	Clear E Pluribus Unum
Medea (Lily\Caster)	Clear Okeanos
Nero Claudius (Saber)	Clear Septem
Nikola Tesla (Archer)	Clear London
Queen Mebd (Rider)	Clear E Pluribus Unum
Quetzalcoatl (Rider)	Clear Babylonia
Rider of Resistance	Clear Agartha
Saber of Empireo	Clear Shimosa
Thomas Edison (Caster)	Clear E Pluribus Unum
Tristan (Archer)	Clear Camelot