Zhukov was involved in Elizabeth's training and she saw him as a surrogate father. He was also Claudia's lover.
He was killed by the CIA as retribution for the Soviet-caused deaths of several FBI agents and a US scientist. Claudia encouraged Elizabeth to avenge his death by assassinating the CIA agent who ordered the killing. ("Covert War") However, Claudia eventually carried this out herself. ("The Colonel")
Zhukov is seen in a flashback giving Philip and Elizabeth their marriage certification before they are married willingly by Father Andrei. ("Darkroom")