Kirei Kotomine's 80 year old father, Risei is a priest in the Church and the regulator of the third and fourth Holy Grail Wars. A friend of Tokiomi Tōsaka's, Risei actively supports him and conspires to ensure that Tokiomi will obtain the Holy Grail in the war, despite the fact that as a member of the Church, he should be ensuring only someone who is worthy of the a powerful artifact like the Grail should be obtaining it.  While he is proud of his son, who has demonstrated himself to be a perfect heir, Risei fails to understand Kirei in any sense. He believes that his son, who has recently lost his wife of two years, may be able to find some purpose in life again by aiding Tokiomi during the Holy Grail War.  Both Risei and Tokiomi, upon discovering that Kirei's command mantra had appeared three years before the start of the war, both came to believe that Kirei was destined to provide Tokiomi with an additional Servant and associated command spells for the upcoming war. Without informing Kirei as to the true nature of the mark that appeared, they transfer Kirei from the Church to the Mages Association as Tokiomi's pupil. Neither man reveals to Kirei that he can also obtain the Holy Grail, instead telling the young man that he is performing a mission for the Church.   ~!According to Kirei Kotomine in Fate, his father died trying to protect him. As revealed in Fate/Zero, after Caster's defeat, Kayneth Archibald El-Melloi approached Risei to obtain additional command spells. After Risei reluctantly gives what Lord El-Melloi has come for, the Master shoots Risei and leaves him to die. As he dies, Risei leaves behind a message containing a secret password that will provide his son with all the remaining command spells Risei could give out. Kirei arrives to find his father dead and his father's final parting gift, and comes to the conclusion that Risei died trying to protect him. Though Kirei sheds tears realizing his father cared about him till the end, he finds himself feeling the same feelings he felt when his wife died - the desire to have seen them die.!~  (Source: Wikipedia)

With the promise of granting any wish, the omnipotent Holy Grail triggered three wars in the past, each too cruel and fierce to leave a victor. In spite of that, the wealthy Einzbern family is confident that the Fourth Holy Grail War will be different; namely, with a vessel of the Holy Grail now in their grasp. Solely for this reason, the much hated "Magus Killer" Kiritsugu Emiya is hired by the Einzberns, with marriage to their only daughter Irisviel as binding contract.
 
Kiritsugu now stands at the center of a cutthroat game of survival, facing off against six other participants, each armed with an ancient familiar, and fueled by unique desires and ideals. Accompanied by his own familiar, Saber, the notorious mercenary soon finds his greatest opponent in Kirei Kotomine, a priest who seeks salvation from the emptiness within himself in pursuit of Kiritsugu.
 
Based on the light novel written by Gen Urobuchi, Fate/Zero depicts the events of the Fourth Holy Grail War—10 years prior to Fate/stay night. Witness a battle royale in which no one is guaranteed to survive.
 
(Source: MAL Rewrite)
 
Note: The first episode aired with a runtime of ~48 minutes as opposed to the standard 24 minute long episode.

As the Fourth Holy Grail War rages on with no clear victor in sight, the remaining Servants and their Masters are called upon by Church supervisor Risei Kotomine, in order to band together and confront an impending threat that could unravel the Grail War and bring about the destruction of Fuyuki City. The uneasy truce soon collapses as Masters demonstrate that they will do anything in their power, no matter how despicable, to win.
 
Seeds of doubt are sown between Kiritsugu Emiya and Saber, his Servant, as their conflicting ideologies on heroism and chivalry clash. Meanwhile, an ominous bond forms between Kirei Kotomine, who still seeks to find his purpose in life, and one of the remaining Servants. As the countdown to the end of the war reaches zero, the cost of winning begins to blur the line between victory and defeat.
 
(Source: MAL Rewrite)

War of the Holy Grail - Pursuing the power of the "Holy Grail" which grants a miracle, this is a contest in which seven magi summon seven Heroic Spirits to compete for it. In that battle whose conclusion was postponed three times, now, the fourth war commenced again. Entrusting their dearest wish of victory, the magi joined the battleground called "Fuyuki", but amongst them, there was a man who was always alone, and could not find out the meaning behind his fights. His name was Kotomine Kirei. Not comprehending the guidance of fate, Kirei was lost, and had kept questioning. Why someone like his was given the Command Seals. However, the fate of his fights crossed Kirei's path with a nemesis by chance. That person is - Emiya Kiritsugu. A man who was sterner than anyone else, more merciless than anyone else, and who sought the miracle of the Holy Grail. 

Merely recited in fragments in Fate/Stay Night, this is the Fourth War of the Holy Grail 10 years ago. The truth which unfolded behind the battle between Shir&#333;'s foster father, Rin's father, and the younger Kotomine Kirei, is finally revealed...

The Fourth Holy Grail War has begun, and seven mages must summon heroes from history to battle each other to the death. Only one mage-and-hero pair will remain to claim the Grail and have their wishes granted! Kiritsugu Emiya was once an assassin but now fights in this war to save the world from those who would destroy it with the Grail’s power. 
(Source: Dark Horse)

Based on the third route of Fate/stay night.