Admiral Alexander Marcus was the head of Starfleet in the mid-23rd century, and a member of Section 31. He was the father of Carol Marcus.
Marcus was the mentor of Christopher Pike and inspired him to join Starfleet.
In 2259, Pike convinced Marcus to alter the punishment for his protégé Captain James T. Kirk, who was being sent back to Starfleet Academy for breaking the Prime Directive. Kirk would instead be demoted to Pike's first officer on the USS Enterprise.
Following the destruction of Vulcan in 2258, Marcus began seeking ways to militarize and better defend the Federation. In particular, he foresaw war with the Klingon Empire as inevitable. Section 31 discovered the SS Botany Bay, and Marcus revived Khan Noonien Singh, recruiting him under the name John Harrison to design weapons and ships.
However, Khan resented Marcus's control over him and the use of his fellow surviving Augments as hostages, and attempted to smuggle them out in the experimental photon torpedoes he created. He was discovered, and Khan was forced to flee alone, beginning a one-man war on the Federation as he presumed Marcus killed his crew.
On stardate 2259.55, Khan coerced Section 31 agent Thomas Harewood into bombing the Kelvin Memorial Archive in London. Marcus received a message from Harewood before he died explaining Harrison threatened him, and the admiral declared a manhunt at a summit in Starfleet Headquarters. Khan, aware protocol dictated a summit like this one, appeared in an attack vehicle and opened fire. Khan was forced to flee however, and Marcus survived, though Pike was killed.
The following morning, Kirk reported Harrison had used the confiscated transwarp beaming formula to escape to Qo'noS. Marcus ordered Kirk to pinpoint and execute Harrison with the 72 experimental photon torpedoes he had designed. Spock deemed Marcus's orders to execute Harrison without trial immoral, and Montgomery Scott found it suspicious that he was not allowed to examine the torpedoes, making Kirk decide to arrest Harrison instead.
Once Kirk discovered the truth from Khan, Marcus showed up in the USS Vengeance - a warship designed by Khan - demanding Kirk hand him over. When Kirk attempted to flee to Earth to put Khan on trial and expose Marcus, the Vengeance caught up and crippled the flagship. Marcus's daughter Carol revealed she was on the Enterprise, but the admiral simply had her beamed up and prepared to wipe out all evidence of his scheme. Fortunately, Scotty had boarded the Vengeance at coordinates given by Khan and deactivated its weapons. Khan and Kirk donned thruster suits and flew over to the ship to commandeer the bridge. Kirk confronted Marcus over his betrayal of everything the Federation stood for, but Khan ended the lesson by knocking him aside and caving in Marcus's skull: the sight prompted screams of horror from Carol.
A year later, Kirk presided over a memorial for those killed the previous year because of the conspiracy.