Ever since the School Island Incident, in which the four Kings were involved, the Silver Clansman, Kuroh Yatogami and Neko were on their search for their master Shiro. Unable to find any leads to Shiro, the two were in a gloomy mood until they ran into Homura members, Rikio Kamamoto and Anna Kushima, who were apparently being chased by someone...
 
(Source: Official Movie Pamphlet)

The manga depicts what happens after the K: Missing Kings film from the viewpoints of different characters. 

(Source: Anime News Network)

In modern Japan, where history has strangely overlapped with reality. There, seven "Kings" with great superpowers existed. Along with their clansman to whom they shared their own power with, the kings each formed clans. Order bound by blue, red flames that cause chaos, irregularities that shine in white, and reforms branched off into green. The Kings, each with their own abilities, now...
The Blue King Reisi Munakata, the leader of the Blue Clan "Scepter 4," held great responsibilities on his back. The tower that Gold King Daikaku Kokujōji supervised called the Dresden Slate was still on his mind, and he felt a great burden by killing the previous Red King, Mikoto Suoh.
 
On the other hand, the former Red Clan "Homra" clansman Anna Kushina experienced the attacks from the Green Clan "jungle" and awakened as the next Red King. By doing this, she bound her comrades through a strong bond once again.
 
Finally, White Clan members Neko and Kuroh believe that the White King Yashiro is still alive, and seek his whereabouts. However, it was not just them searching for the White King. The Green King Nagare Hisui once again...
 
With "jungle" once again jumping back into action, the fates of the various Kings are brought together.

The story takes place in a world where seven people with unusual powers are crowned as “kings,” and revolves around the “bonds” and “fate” between the people involved.
 
(Source: Anime News Network)

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